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subscript="b3">T</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:id xml:space="preserve" subscript="01">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="12">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="44"/> </region> <region region-id="2079" left="36" top="1994.25" width="578.25" height="12" align-x="43.5" align-y="2004" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Pro sestavení rovnic inverzní úlohy je celková transformační matice vyjádřena symbolickým vynásobením jednotlivých matic </text> </region> <region region-id="1452" left="36" top="2031" width="390.75" height="72" align-x="60.75" align-y="2070" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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align-y="2412" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:indexer/> <ml:apply> <ml:id xml:space="preserve">Q</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:sequence> </ml:apply> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="53"/> </region> <region region-id="536" left="42" top="2426.25" width="140.25" height="19.5" align-x="73.5" align-y="2436" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:indexer/> <ml:apply> <ml:id xml:space="preserve">Q</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:sequence> </ml:apply> <ml:sequence> <ml:real>2</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="54"/> </region> <region region-id="537" left="42" 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use-page-width="false" push-down="false" lock-width="true"> rychlosti </text> </region> <region region-id="568" left="18" top="2568" width="93" height="31.5" align-x="61.5" align-y="2586" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="569" left="120" top="2568" width="93" height="31.5" align-x="163.5" align-y="2586" show-border="false" 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push-down="false" lock-width="true"> Kontrola v Pro/E </text> </region> <region region-id="1729" left="552" top="2646" width="259.5" height="217.5" align-x="552" align-y="2646" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="62"/> <rendering item-idref="63"/> </region> <region region-id="1726" left="6" top="2652" width="238.5" height="211.5" align-x="6" align-y="2652" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="64"/> <rendering item-idref="65"/> </region> <region region-id="1212" left="276" top="2652" width="251.25" height="205.5" align-x="276" align-y="2652" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="66"/> <rendering item-idref="67"/> </region> <region region-id="1768" left="12" top="2868" width="312.75" height="345.75" align-x="12" align-y="2868" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <metafile mapping-mode="8" x-extent="311.2441" y-extent="344.2394" item-idref="68"/> </picture> <rendering item-idref="69"/> </region> <region region-id="1770" left="354" top="2868" width="312.75" height="345.75" align-x="354" align-y="2868" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <metafile mapping-mode="8" x-extent="311.2441" y-extent="344.2394" item-idref="70"/> </picture> <rendering item-idref="71"/> </region> <region region-id="1772" left="690" top="2868" width="312.75" height="345.75" align-x="690" align-y="2868" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <metafile mapping-mode="8" x-extent="311.2441" y-extent="344.2394" item-idref="72"/> 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top="4418.25" width="120.75" height="12" align-x="42" align-y="4428" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> vektory na osách z </text> </region> <region region-id="2230" left="48" top="4448.25" width="158.25" height="15.75" align-x="78.75" align-y="4458" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="0">k</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">submatrix</ml:id> <ml:sequence> <ml:id xml:space="preserve" subscript="b0">T</ml:id> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>3</ml:real> <ml:real>3</ml:real> </ml:sequence> </ml:apply> 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width="68.25" height="49.5" align-x="81" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="0">k</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="109"/> </region> <region region-id="2178" left="228" top="4538.25" width="68.25" height="49.5" align-x="261" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="1">k</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="110"/> </region> <region region-id="2217" left="420" top="4538.25" width="68.25" height="49.5" align-x="453" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="2">k</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>1.2246063538223773E-16</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="111"/> </region> <region region-id="2176" left="618" top="4538.25" width="68.25" height="49.5" align-x="651" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="3">k</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>1.2246063538223773E-16</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="112"/> </region> <region region-id="2245" left="48" top="4616.25" width="159" height="12" align-x="48" align-y="4626" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Submatice rotace </text> </region> <region region-id="2244" left="48" top="4652.25" width="153" height="15.75" align-x="73.5" align-y="4662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="b0">R</ml:id> <ml:apply> <ml:id xml:space="preserve">submatrix</ml:id> <ml:sequence> <ml:id xml:space="preserve" subscript="b0">T</ml:id> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="113"/> </region> <region region-id="2220" left="228" top="4652.25" width="178.5" height="15.75" align-x="266.25" align-y="4662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="b1">R</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">submatrix</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve" subscript="b1">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="114"/> </region> <region region-id="2216" left="420" top="4652.25" width="178.5" height="15.75" align-x="458.25" align-y="4662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="b2">R</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">submatrix</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve" subscript="b2">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="115"/> </region> <region region-id="2213" left="618" top="4652.25" width="178.5" height="15.75" align-x="656.25" align-y="4662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="b3">R</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">submatrix</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve" subscript="b3">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="116"/> </region> <region region-id="2243" left="48" top="4694.25" width="204.75" height="12" align-x="48" align-y="4704" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> vzájemná (relativní) úhlová rychlost </text> </region> <region region-id="2242" left="48" top="4730.25" width="62.25" height="49.5" align-x="81" align-y="4758" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> 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</ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="121"/> </region> <region region-id="841" left="258" top="4796.25" width="126" height="12" align-x="258" align-y="4806" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> v zákl. ss. </text> </region> <region region-id="2240" left="48" top="4820.25" width="111" height="15.75" align-x="81" align-y="4830" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="2">ω</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="12">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="122"/> </region> <region region-id="843" left="258" top="4820.25" width="138" height="12" align-x="258" align-y="4830" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> v zákl. ss. </text> </region> <region region-id="2239" left="48" top="4844.25" width="111" height="15.75" align-x="81" align-y="4854" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">ω</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="23">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="123"/> </region> <region region-id="845" left="258" top="4844.25" width="111" height="12" align-x="258" align-y="4854" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> v zákl. ss. </text> </region> <region region-id="2436" left="48" top="4898.25" width="150" height="12" align-x="48" align-y="4908" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">vektory mezi počátky ss</inlineAttr> </f> </text> </region> <region region-id="2437" left="48" top="4934.25" width="204.75" height="15.75" align-x="84.75" align-y="4944" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="01">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="b0">R</ml:id> <ml:apply> <ml:id xml:space="preserve">submatrix</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve" subscript="01">A</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>4</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="124"/> </region> <region region-id="2448" left="282" top="4934.25" width="217.5" 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background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Vektor do koncového bodu </text> </region> <region region-id="2481" left="48" top="5366.25" width="207" height="15.75" align-x="84.75" align-y="5376" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="03">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">submatrix</ml:id> <ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve" subscript="b3">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="b0">T</ml:id> </ml:apply> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>4</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="142"/> </region> <region region-id="2482" left="48" top="5414.25" width="162.75" height="12" align-x="48" align-y="5424" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Rychlost článku 0 - podstavce</inlineAttr> </f> </text> </region> <region region-id="2483" left="48" top="5438.25" width="60" height="49.5" align-x="78.75" align-y="5466" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="0">v</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> 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<text use-page-width="false" push-down="false" lock-width="true"> v zákl. ss. </text> </region> <region region-id="2925" left="48" top="5582.25" width="82.5" height="49.5" align-x="95.25" align-y="5610" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="01">v</ml:id> <ml:real>0.1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="147"/> </region> <region region-id="2926" left="348" top="5582.25" width="91.5" height="49.5" align-x="395.25" align-y="5610" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="12">v</ml:id> <ml:real>0.1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.49999999999999434</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="148"/> </region> <region region-id="2927" left="690" top="5582.25" width="109.5" height="49.5" align-x="737.25" align-y="5610" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="23">v</ml:id> <ml:real>0.1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>-0.013090080263343719</ml:real> <ml:real>0.54233999302057734</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="149"/> </region> <region region-id="2900" left="48" top="5666.25" width="746.25" height="12" align-x="48" align-y="5676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Vzájemné rychlosti univerzální obecný tvar - vystupuje zde parciální derivace vektoru p podle kloubové proměnné q - pomocí diferenciálních operátorů</inlineAttr> </f> </text> </region> <region region-id="2920" left="54" top="5699.25" width="96.75" height="67.5" align-x="72.75" align-y="5736" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" 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<ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="155"/> </region> <region region-id="2894" left="348" top="5816.25" width="91.5" height="49.5" align-x="395.25" align-y="5844" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="12">v</ml:id> <ml:real>0.1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.49999999999999434</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="156"/> </region> <region region-id="2830" left="690" top="5816.25" width="109.5" height="49.5" align-x="737.25" align-y="5844" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="23">v</ml:id> <ml:real>0.1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>-0.013090080263343719</ml:real> <ml:real>0.54233999302057734</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="157"/> </region> <region region-id="2934" left="48" top="5906.25" width="849.75" height="12" align-x="75.75" align-y="5916" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Alternativně nejprve derivace vektoru p23 v lokálním souřadném systému, výsledkem je vektor rychlosti v lokálním ss., ten se vyjádří v základním ss. jen násobením submaticí rotace </text> </region> <region region-id="2933" left="48" top="5936.25" width="275.25" height="15.75" align-x="84" align-y="5946" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="23">v</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="b2">R</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">submatrix</ml:id> <ml:sequence> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="t">D</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> <ml:real>3</ml:real> 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zrychlení článků </text> </region> <region region-id="899" left="42" top="6524.25" width="60" height="49.5" align-x="72.75" align-y="6552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="0">ε</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="181"/> </region> <region region-id="2954" left="126" top="6542.25" width="113.25" height="15.75" align-x="162" align-y="6552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="01">ε</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="0">k</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="182"/> </region> <region region-id="2955" left="252" top="6524.25" width="65.25" height="49.5" align-x="288" align-y="6552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="12">ε</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="183"/> </region> <region region-id="2956" left="342" top="6524.25" width="65.25" height="49.5" align-x="378" align-y="6552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="23">ε</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="184"/> </region> <region region-id="904" left="42" top="6596.25" width="184.5" height="15.75" align-x="72.75" align-y="6606" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">ε</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="0">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="185"/> </region> <region region-id="905" left="42" top="6620.25" width="184.5" height="15.75" align-x="72.75" align-y="6630" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="2">ε</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="12">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="12">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="186"/> </region> <region region-id="2957" left="42" top="6644.25" width="184.5" height="15.75" align-x="72.75" align-y="6654" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">ε</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="23">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="23">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="187"/> </region> <region region-id="2966" left="42" top="6692.25" width="465" height="12" align-x="42" align-y="6702" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Výpočet relativních translačních zrychlení počátků lokálních souřadných systémů</inlineAttr> </f> </text> </region> <region region-id="3010" left="42" top="6728.25" width="60.75" height="49.5" align-x="73.5" align-y="6756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="0">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="188"/> </region> <region region-id="3021" left="192" top="6746.25" width="250.5" height="12" align-x="216.75" align-y="6756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Translační zrychlení pošátku lokálního ss. podstavce </text> </region> <region region-id="3023" left="42" top="6806.25" width="248.25" height="15.75" align-x="78.75" align-y="6816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="01">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="01">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="01">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="01">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="189"/> </region> <region region-id="3022" left="390" top="6806.25" width="107.25" height="12" align-x="390" align-y="6816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Pro rotační</inlineAttr> </f> </text> </region> <region region-id="3026" left="42" top="6866.25" width="114" height="15.75" align-x="78.75" align-y="6876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="12">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">k</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="2">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="190"/> </region> <region region-id="3025" left="198" top="6847.5" width="96" height="51.75" align-x="234.75" align-y="6876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="12">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:id xml:space="preserve" subscript="2">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="191"/> </region> <region region-id="3024" left="390" top="6866.25" width="105.75" height="12" align-x="390" align-y="6876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Translační</inlineAttr> </f> </text> </region> <region region-id="3033" left="42" top="6932.25" width="114" height="15.75" align-x="78.75" align-y="6942" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="23">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="2">k</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="192"/> </region> <region region-id="3034" left="198" top="6912" width="159.75" height="54" align-x="234.75" align-y="6942" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="23">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="193"/> </region> <region region-id="3035" left="390" top="6932.25" width="88.5" height="12" align-x="390" align-y="6942" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Translační</inlineAttr> </f> </text> </region> <region region-id="3037" left="42" top="6998.25" width="332.25" height="12" align-x="60.75" align-y="7008" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výpočet translačních zrychlení počátků lokálních souřadných systémů </text> </region> <region region-id="920" left="42" top="7040.25" width="406.5" height="15.75" align-x="73.5" align-y="7050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="0">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:parens> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">v</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="194"/> </region> <region region-id="921" left="42" top="7070.25" width="406.5" height="15.75" align-x="73.5" align-y="7080" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="12">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="12">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:parens> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="12">v</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="12">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="195"/> </region> <region region-id="922" left="42" top="7100.25" width="406.5" height="15.75" align-x="73.5" align-y="7110" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="23">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="23">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:parens> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="23">v</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="23">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="196"/> </region> <region region-id="3046" left="42" top="7142.25" width="493.5" height="12" align-x="42" align-y="7152" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Kontrola zrychlení - odpovídá zadání ax, ay a az - definice pohybu konc. bodu na začátku výpočtu </text> </region> <region region-id="3346" left="168" top="7190.25" width="47.25" height="192" align-x="168.75" align-y="7200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">t</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>0</ml:real> <ml:real>0.02</ml:real> <ml:real>0.04</ml:real> <ml:real>0.06</ml:real> <ml:real>0.08</ml:real> <ml:real>0.1</ml:real> <ml:real>0.12</ml:real> <ml:real>0.14</ml:real> <ml:real>0.16</ml:real> <ml:real>0.18</ml:real> <ml:real>0.2</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="197"/> </resultFormat> </math> <rendering item-idref="198"/> </region> <region region-id="3347" left="216" top="7190.25" width="41.25" height="198" align-x="235.5" align-y="7200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:apply> <ml:id xml:space="preserve" subscript="3">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>-4.999999999891422</ml:real> <ml:real>-5.0000000000921769</ml:real> <ml:real>-4.9999999999007212</ml:real> <ml:real>-5.0000000000463842</ml:real> <ml:real>-4.9999999999707541</ml:real> <ml:real>-5.0000000000230775</ml:real> <ml:real>-5.0000000000181695</ml:real> <ml:real>-5.0000000000260219</ml:real> <ml:real>-5.000000000034694</ml:real> <ml:real>-5.0000000000177716</ml:real> <ml:real>-4.9999999999848654</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="199"/> </resultFormat> </math> <rendering item-idref="200"/> </region> <region region-id="3348" left="288" top="7190.25" width="41.25" height="198" align-x="307.5" align-y="7200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:apply> <ml:id xml:space="preserve" subscript="3">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:sequence> <ml:real>2</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>4.9999999997850155</ml:real> <ml:real>4.999999999467458</ml:real> <ml:real>5.0000000000728679</ml:real> <ml:real>4.9999999999808518</ml:real> <ml:real>5.0000000001221592</ml:real> <ml:real>4.9999999999883524</ml:real> <ml:real>5.00000000000407</ml:real> <ml:real>4.9999999999764455</ml:real> <ml:real>5.0000000000196021</ml:real> <ml:real>4.9999999999824629</ml:real> <ml:real>5.000000000006688</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="201"/> </resultFormat> </math> <rendering item-idref="202"/> </region> <region region-id="3349" left="366" top="7190.25" width="41.25" height="198" align-x="385.5" align-y="7200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:apply> <ml:id xml:space="preserve" subscript="3">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:sequence> <ml:real>3</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>5.000000000007577</ml:real> <ml:real>5.0000000001619131</ml:real> <ml:real>5.0000000000171063</ml:real> <ml:real>4.9999999999998659</ml:real> <ml:real>5.0000000000006395</ml:real> <ml:real>5.0000000000003268</ml:real> <ml:real>4.9999999999994484</ml:real> <ml:real>5.0000000000007754</ml:real> <ml:real>5.0000000000005711</ml:real> <ml:real>5.0000000000001377</ml:real> <ml:real>5.0000000000001616</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="203"/> </resultFormat> </math> <rendering item-idref="204"/> </region> <region region-id="3053" left="42" top="7190.25" width="75" height="49.5" align-x="75.75" align-y="7218" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="3">a</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>-4.999999999891422</ml:real> <ml:real>4.9999999997850155</ml:real> <ml:real>5.000000000007577</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="205"/> </region> <region region-id="3352" left="42" top="7400.25" width="636.75" height="36" align-x="55.5" align-y="7410" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Tento úkon kontroly je velmi důležitý, pohyb koncového bodu byl řešením inverzní úlohy rozložen do jednotlivých kloubů, byly vypočteny průběhy rychlostí a zrychlení (translační i rotační) a ve zrychlení a3 se všechny veličiny skládají. Pokud tato veličina je shodná se zadáním, je jistota správnosti výpočtu až po toto místo řešení </text> </region> <region region-id="3406" left="42" top="7484.25" width="129" height="12" align-x="42" align-y="7494" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Poloha težišť z Pro/E</inlineAttr> </f> </text> </region> <region region-id="3708" left="42" top="7514.25" width="303" height="24" align-x="42" align-y="7524" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> CENTER OF GRAVITY with respect to LCS1 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="4"/>-4.0325987e-02 -1.8024766e-06<sp count="2"/>7.3574162e-01<sp count="2"/>M </text> </region> <region region-id="3704" left="384" top="7514.25" width="304.5" height="24" align-x="384" align-y="7524" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> CENTER OF GRAVITY with respect to LCS2 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="4"/>-7.2368752e-02<sp count="2"/>0.0000000e+00 -4.7439674e-02<sp count="2"/>M </text> </region> <region region-id="3701" left="732" top="7514.25" width="314.25" height="24" align-x="732" align-y="7524" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> CENTER OF GRAVITY with respect to LCS3 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="5"/>2.5740416e-03<sp count="2"/>0.0000000e+00 -3.7039760e-01<sp count="2"/>M </text> </region> <region region-id="3711" left="42" top="7562.25" width="124.5" height="21.75" align-x="66.75" align-y="7578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t11">x</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> <ml:real>4.0325987</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="206"/> </region> <region region-id="3710" left="384" top="7562.25" width="124.5" height="21.75" align-x="408.75" align-y="7578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t22">x</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> 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optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t11">y</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> <ml:real>1.8024766</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-6</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="209"/> </region> <region region-id="3713" left="384" top="7592.25" width="85.5" height="15.75" align-x="409.5" align-y="7602" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t22">y</ml:id> <ml:real>0.0000000</ml:real> </ml:define> </math> <rendering item-idref="210"/> </region> <region region-id="3712" left="732" top="7592.25" width="103.5" height="15.75" align-x="757.5" align-y="7602" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t33">y</ml:id> <ml:real>0.0000000000</ml:real> </ml:define> </math> <rendering item-idref="211"/> </region> <region region-id="3717" left="42" top="7610.25" width="118.5" height="21.75" align-x="66.75" align-y="7626" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t11">z</ml:id> <ml:apply> <ml:mult/> <ml:real>7.3574162</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="212"/> </region> <region region-id="3716" left="384" top="7610.25" width="124.5" height="21.75" align-x="408.75" align-y="7626" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t22">z</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> <ml:real>4.7439674</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="213"/> </region> <region region-id="3715" left="732" top="7610.25" width="124.5" height="21.75" align-x="756.75" align-y="7626" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t33">z</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> <ml:real>3.7039760</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="214"/> </region> <region region-id="973" left="30" top="7688.25" width="152.25" height="12" align-x="30" align-y="7698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">vektory do těžiště v lokálních ss</inlineAttr> </f> </text> </region> <region region-id="3735" left="210" top="7667.25" width="67.5" height="56.25" align-x="236.25" align-y="7698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t11">p</ml:id> <ml:matrix rows="3" cols="1"> <ml:id xml:space="preserve" subscript="t11">x</ml:id> <ml:id xml:space="preserve" subscript="t11">y</ml:id> <ml:id xml:space="preserve" subscript="t11">z</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="215"/> </region> <region region-id="3729" left="306" top="7667.25" width="67.5" height="56.25" align-x="332.25" align-y="7698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t22">p</ml:id> <ml:matrix rows="3" cols="1"> <ml:id xml:space="preserve" subscript="t22">x</ml:id> <ml:id xml:space="preserve" subscript="t22">y</ml:id> <ml:id xml:space="preserve" subscript="t22">z</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="216"/> </region> <region region-id="3730" left="402" top="7667.25" width="67.5" height="56.25" align-x="428.25" align-y="7698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t33">p</ml:id> <ml:matrix rows="3" cols="1"> <ml:id xml:space="preserve" subscript="t33">x</ml:id> <ml:id xml:space="preserve" subscript="t33">y</ml:id> <ml:id xml:space="preserve" subscript="t33">z</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="217"/> </region> <region region-id="3749" left="30" top="7760.25" width="156.75" height="24" align-x="30" align-y="7770" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">je nutno přepočítat do základního ss</inlineAttr> </f> </text> </region> <region region-id="3736" left="210" top="7760.25" width="106.5" height="15.75" align-x="249" align-y="7770" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="t1b">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="b1">R</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t11">p</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="218"/> </region> <region region-id="3737" left="210" top="7784.25" width="106.5" height="15.75" align-x="249" align-y="7794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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height="67.5" align-x="345" align-y="8070" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="t3b">P</ml:id> <ml:real>0.0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="1"> <ml:real>-0.067574041599999926</ml:real> <ml:real>0.6396024</ml:real> <ml:real>1.454</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="229"/> </region> <region region-id="3762" left="30" top="8132.25" width="300" height="12" align-x="30" align-y="8142" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr 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z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> MASS =<sp count="2"/>4.8824683e+01 KILOGRAM CENTER OF GRAVITY with respect to LCS1 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="4"/>-4.0325987e-02 -1.8024766e-06<sp count="2"/>7.3574162e-01<sp count="2"/>M INERTIA with respect to LCS1 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>4.6443693e+01 -7.9670815e-06<sp count="2"/>2.0478701e+00 Iyx Iyy Iyz -7.9670815e-06<sp count="2"/>4.7356949e+01<sp count="2"/>1.4573962e-04 Izx Izy Izz<sp count="2"/>2.0478701e+00<sp count="2"/>1.4573962e-04<sp count="2"/>1.4139746e+00 INERTIA at CENTER OF GRAVITY with respect to LCS1 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>2.0014124e+01 -4.4181788e-06<sp count="2"/>5.9926583e-01 Iyx Iyy Iyz -4.4181788e-06<sp count="2"/>2.0847982e+01<sp count="2"/>8.0990420e-05 Izx Izy Izz<sp count="2"/>5.9926583e-01<sp count="2"/>8.0990420e-05<sp count="2"/>1.3345766e+00 </text> </region> <region region-id="3928" left="30" top="9224.25" width="393" height="12" align-x="30" align-y="9234" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Článek ROT1 - matice setrvačnosti k těžišti, vyjádřeno (orientace) podle LCS1</inlineAttr> </f> </text> </region> <region region-id="3929" left="30" top="9254.25" width="105" height="15.75" align-x="51" align-y="9264" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">m</ml:id> <ml:real>48.8246830000</ml:real> </ml:define> </math> <rendering 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width="140.25" height="21.75" align-x="60" align-y="9534" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">J</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="b1">R</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="11">J</ml:id> </ml:apply> <ml:apply> <ml:transpose/> <ml:apply> <ml:id xml:space="preserve" subscript="b1">R</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="254"/> </region> <region region-id="3978" left="192" top="9497.25" width="267" height="67.5" align-x="224.25" align-y="9534" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="1">J</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="3"> <ml:real>20.014124</ml:real> <ml:real>4.4181788001021146E-06</ml:real> <ml:real>0.59926583000000011</ml:real> <ml:real>4.4181788001021146E-06</ml:real> <ml:real>20.847982</ml:real> <ml:real>8.0990419999926624E-05</ml:real> <ml:real>0.59926583000000011</ml:real> <ml:real>8.0990419999926624E-05</ml:real> <ml:real>1.3345766</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="255"/> </region> <region region-id="1662" left="36" top="9606" width="205.5" height="166.5" align-x="36" align-y="9606" show-border="false" show-highlight="false" is-protected="true" 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xml:space="preserve" subscript="x2t">J</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xy2t">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xz2t">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xy2t">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="y2t">J</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="yz2t">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xz2t">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="yz2t">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="z2t">J</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="265"/> </region> <region region-id="4024" left="204" top="10232.25" width="160.5" height="49.5" align-x="225.75" align-y="10260" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="22">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="3"> <ml:real>0.93795366</ml:real> <ml:real>0</ml:real> <ml:real>-0.025398594</ml:real> <ml:real>0</ml:real> <ml:real>1.4723852</ml:real> <ml:real>0</ml:real> <ml:real>-0.025398594</ml:real> <ml:real>0</ml:real> <ml:real>1.2367697</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="266"/> </region> <region region-id="4007" left="30" top="10310.25" width="273" height="12" align-x="30" align-y="10320" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Matice setrvačnosti přepočtená do základního GCS</inlineAttr> </f> </text> </region> <region region-id="4008" left="30" top="10352.25" width="140.25" height="21.75" align-x="60" align-y="10368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="2">J</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="b2">R</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="22">J</ml:id> </ml:apply> <ml:apply> <ml:transpose/> <ml:apply> <ml:id xml:space="preserve" subscript="b2">R</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="267"/> </region> <region region-id="4023" left="204" top="10340.25" width="159" height="49.5" align-x="236.25" align-y="10368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="2">J</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="3"> <ml:real>0.93795366</ml:real> <ml:real>0.025398594000000038</ml:real> <ml:real>0</ml:real> <ml:real>0.025398594000000038</ml:real> <ml:real>1.2367697</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1.4723852</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="268"/> </region> <region region-id="1677" left="36" top="10446" width="341.25" height="165" align-x="36" align-y="10446" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <metafile mapping-mode="8" x-extent="339.7606" y-extent="163.5024" item-idref="269"/> </picture> <rendering item-idref="270"/> </region> <region region-id="4031" left="36" top="10628.25" width="507" height="240" align-x="36" align-y="10638" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> TRAN3 MASS =<sp count="2"/>5.9261161e+01 KILOGRAM CENTER OF GRAVITY with respect to LCS3 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="5"/>2.5740416e-03<sp count="2"/>0.0000000e+00 -3.7039760e-01<sp count="2"/>M INERTIA with respect to LCS3 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>3.3435680e+01<sp count="2"/>0.0000000e+00<sp count="2"/>1.9296398e-01 Iyx Iyy Iyz<sp count="2"/>0.0000000e+00<sp count="2"/>3.4142950e+01<sp count="2"/>0.0000000e+00 Izx Izy 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lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Matice setrvačnosti přepočtená do základního GCS</inlineAttr> </f> </text> </region> <region region-id="4071" left="36" top="11204.25" width="140.25" height="21.75" align-x="66" align-y="11220" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">J</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="b3">R</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="33">J</ml:id> </ml:apply> <ml:apply> <ml:transpose/> <ml:apply> <ml:id xml:space="preserve" subscript="b3">R</ml:id> <ml:id xml:space="preserve">t</ml:id> 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tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">G</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-9.80665</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="286"/> </region> <region region-id="1554" left="42" top="11576.25" width="180" height="12" align-x="42" align-y="11586" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Rovnováha sil - třetí článek</inlineAttr> </f> </text> </region> <region region-id="1555" left="42" top="11600.25" width="163.5" height="15.75" align-x="70.5" align-y="11610" show-border="false" show-highlight="false" 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xml:space="preserve" subscript="0">l</ml:id> <ml:real>1</ml:real> </ml:matrix> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="371"/> </region> <region region-id="72" left="24" top="16821" width="288" height="72" align-x="67.5" align-y="16860" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="b1">dT</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="372"/> </region> <region region-id="4227" left="24" top="16940.25" width="412.5" height="12" align-x="42.75" align-y="16950" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Výpočet totálního diferenciálu (analogie derivace) transformační matice Tb2 podle času </text> </region> <region region-id="73" left="30" top="16977" width="511.5" height="142.5" align-x="73.5" align-y="17016" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="b2">dT</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="0">l</ml:id> <ml:real>1</ml:real> </ml:matrix> <ml:parens> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> </ml:matrix> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="2">l</ml:id> <ml:real>0</ml:real> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:matrix> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> </ml:matrix> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </ml:apply> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="2">l</ml:id> <ml:real>0</ml:real> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:matrix> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="373"/> </region> <region region-id="74" left="30" top="17168.25" width="383.25" height="74.25" align-x="73.5" align-y="17208" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="b2">dT</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">l</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">l</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="374"/> </region> <region region-id="4238" left="30" top="17282.25" width="412.5" height="12" align-x="48.75" align-y="17292" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výpočet totálního diferenciálu (analogie derivace) transformační matice Tb3 podle času </text> </region> <region region-id="4240" left="30" top="17313" width="601.5" height="213" align-x="73.5" align-y="17352" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="b3">dT</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="0">l</ml:id> <ml:real>1</ml:real> </ml:matrix> <ml:parens> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> 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subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">l</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="376"/> </region> <region region-id="1896" left="30" top="17702.25" width="453.75" height="228" align-x="30" align-y="17712" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> ROT1 MASS =<sp count="2"/>4.8824683e+01 KILOGRAM CENTER OF GRAVITY with respect to LCS1 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="4"/>-4.0325987e-02 -1.8024766e-06<sp count="2"/>7.3574162e-01<sp count="2"/>M INERTIA with respect to LCS1 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>4.6443693e+01 -7.9670815e-06<sp count="2"/>2.0478701e+00 Iyx Iyy Iyz -7.9670815e-06<sp count="2"/>4.7356949e+01<sp count="2"/>1.4573962e-04 Izx Izy Izz<sp count="2"/>2.0478701e+00<sp count="2"/>1.4573962e-04<sp count="2"/>1.4139746e+00 INERTIA at CENTER OF GRAVITY with respect to LCS1 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>2.0014124e+01 -4.4181788e-06<sp count="2"/>5.9926583e-01 Iyx Iyy Iyz -4.4181788e-06<sp count="2"/>2.0847982e+01<sp count="2"/>8.0990420e-05 Izx Izy Izz<sp count="2"/>5.9926583e-01<sp count="2"/>8.0990420e-05<sp count="2"/>1.3345766e+00 </text> </region> <region region-id="4265" 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top="18134.25" width="118.5" height="21.75" align-x="216.75" align-y="18150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yz1">J</ml:id> <ml:apply> <ml:mult/> <ml:real>1.4573962</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-4</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="382"/> </region> <region region-id="4293" left="348" top="18140.25" width="81" height="15.75" align-x="369" align-y="18150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="z1">J</ml:id> <ml:real>1.4139746</ml:real> </ml:define> </math> <rendering item-idref="383"/> </region> <region region-id="4366" left="30" top="18188.25" width="354.75" height="12" align-x="51" align-y="18198" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Přepočet momentů setrvačnosti k osám na momenty setrvačnosti k rovinám </text> </region> <region region-id="4257" left="30" top="18214.5" width="102.75" height="31.5" align-x="54.75" align-y="18234" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="xx1">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="y1">J</ml:id> <ml:id xml:space="preserve" subscript="z1">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="x1">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="384"/> </region> <region region-id="4258" left="30" top="18250.5" width="102.75" height="31.5" align-x="54.75" align-y="18270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yy1">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="z1">J</ml:id> <ml:id xml:space="preserve" subscript="x1">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="y1">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="385"/> </region> <region region-id="4259" left="192" top="18230.25" width="68.25" height="74.25" align-x="219" align-y="18270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t11">P</ml:id> <ml:matrix rows="4" cols="1"> <ml:id xml:space="preserve" subscript="t11">x</ml:id> <ml:id xml:space="preserve" subscript="t11">y</ml:id> <ml:id xml:space="preserve" subscript="t11">z</ml:id> <ml:real>1</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="386"/> </region> <region region-id="4260" left="300" top="18230.25" width="124.5" height="73.5" align-x="326.25" align-y="18270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t11">P</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="1"> <ml:real>-0.040325987</ml:real> <ml:real>-1.8024766E-06</ml:real> <ml:real>0.7357416200000001</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="387"/> </region> <region region-id="4261" left="30" top="18286.5" width="102.75" height="31.5" align-x="54.75" align-y="18306" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="zz1">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="x1">J</ml:id> <ml:id xml:space="preserve" subscript="y1">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="z1">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="388"/> </region> <region region-id="4368" left="30" top="18326.25" width="135.75" height="12" align-x="50.25" align-y="18336" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Normální matice setrvačnosti </text> </region> <region region-id="93" left="30" top="18353.25" width="126.75" height="56.25" align-x="47.25" align-y="18384" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">J</ml:id> <ml:matrix rows="3" cols="3"> <ml:id xml:space="preserve" subscript="x1">J</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xy1">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xz1">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xy1">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="y1">J</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="yz1">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xz1">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="yz1">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="z1">J</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="389"/> </region> <region region-id="285" left="180" top="18347.25" width="263.25" height="67.5" align-x="196.5" align-y="18384" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="3"> <ml:real>46.443693</ml:real> <ml:real>7.9670815E-06</ml:real> <ml:real>-2.0478701</ml:real> <ml:real>7.9670815E-06</ml:real> <ml:real>47.356949</ml:real> <ml:real>-0.00014573962</ml:real> <ml:real>-2.0478701</ml:real> <ml:real>-0.00014573962</ml:real> <ml:real>1.4139746</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="390"/> </region> <region region-id="4370" left="30" top="18428.25" width="147.75" height="12" align-x="56.25" align-y="18438" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Homogenní matice setrvačnosti </text> </region> <region region-id="95" left="24" top="18456.75" width="228" height="76.5" align-x="43.5" align-y="18498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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subscript="t11">z</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">m</ml:id> <ml:id xml:space="preserve" subscript="t11">x</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">m</ml:id> <ml:id xml:space="preserve" subscript="t11">y</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">m</ml:id> <ml:id xml:space="preserve" subscript="t11">z</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="1">m</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="391"/> </region> <region region-id="96" left="270" top="18449.25" width="342.75" height="91.5" align-x="288.75" align-y="18498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">H</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>1.1636153</ml:real> <ml:real>-7.9670815E-06</ml:real> <ml:real>2.0478701</ml:real> <ml:real>-1.9689035319371211</ml:real> <ml:real>-7.9670815E-06</ml:real> <ml:real>0.25035930000000306</ml:real> <ml:real>0.00014573962</ml:real> <ml:real>-8.80053486099178E-05</ml:real> <ml:real>2.0478701</ml:real> <ml:real>0.00014573962</ml:real> <ml:real>46.193333700000004</ml:real> <ml:real>35.922351366406467</ml:real> <ml:real>-1.9689035319371211</ml:real> <ml:real>-8.80053486099178E-05</ml:real> <ml:real>35.922351366406467</ml:real> <ml:real>48.824683</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="392"/> </region> <region region-id="97" left="24" top="18572.25" width="194.25" height="12" align-x="24" align-y="18582" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Kinetická energie prvního článku</inlineAttr> </f> </text> </region> <region region-id="98" left="24" top="18594.75" width="183.75" height="29.25" align-x="56.25" align-y="18612" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">tr</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="b1">dT</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="1">H</ml:id> </ml:apply> <ml:apply> <ml:transpose/> <ml:apply> <ml:id xml:space="preserve" subscript="b1">dT</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="393"/> </region> <region region-id="99" left="24" top="18638.25" width="669.75" height="12" align-x="24" align-y="18648" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Pro odvození výrazu pro kinetickou energii pro ruční použití v Lagr.rov. II. druhu provedeme symbolicky roznásobení (Shift+F9) </text> </region> <region region-id="100" left="24" top="18669" width="770.25" height="80.25" align-x="56.25" align-y="18714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">tr</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> 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<ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="394"/> </region> <region region-id="1059" left="24" top="18774.75" width="1531.5" height="29.25" align-x="56.25" align-y="18792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" 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xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="xy1">J</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="xy1">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="yy1">J</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="xx1">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="xy1">J</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="xy1">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="yy1">J</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="395"/> </region> <region region-id="1060" left="24" top="18816.75" width="213" height="29.25" align-x="56.25" align-y="18834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="xx1">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="yy1">J</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="396"/> </region> <region region-id="103" left="24" top="18858.75" width="158.25" height="29.25" align-x="56.25" align-y="18876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="xx1">J</ml:id> <ml:id xml:space="preserve" subscript="yy1">J</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="397"/> </region> <region region-id="104" left="24" top="18894.75" width="117" height="29.25" align-x="56.25" align-y="18912" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="z1">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="398"/> </region> <region region-id="105" left="192" top="18902.25" width="79.5" height="12" align-x="192" align-y="18912" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> jen rotace </text> </region> <region region-id="1898" left="24" top="18962.25" width="474" height="228" align-x="24" align-y="18972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> TRAN2 MASS =<sp count="2"/>4.2894906e+01 KILOGRAM CENTER OF GRAVITY with respect to LCS2 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="4"/>-7.2368752e-02<sp count="2"/>0.0000000e+00 -4.7439674e-02<sp count="2"/>M INERTIA with respect to LCS2 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>1.0344896e+00<sp count="2"/>0.0000000e+00 -1.2186605e-01 Iyx Iyy Iyz<sp count="2"/>0.0000000e+00<sp count="2"/>1.7935719e+00<sp count="2"/>0.0000000e+00 Izx Izy Izz -1.2186605e-01<sp count="2"/>0.0000000e+00<sp count="2"/>1.4614205e+00 INERTIA at CENTER OF GRAVITY with respect to LCS2 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>9.3795366e-01<sp count="2"/>0.0000000e+00<sp count="2"/>2.5398594e-02 Iyx Iyy Iyz<sp count="2"/>0.0000000e+00<sp count="2"/>1.4723852e+00<sp count="2"/>0.0000000e+00 Izx Izy Izz<sp count="2"/>2.5398594e-02<sp count="2"/>0.0000000e+00<sp count="2"/>1.2367697e+00 </text> </region> <region region-id="4303" left="24" top="19226.25" width="129" height="24" align-x="24" align-y="19236" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Článek 2</inlineAttr> </f> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">momenty k lokálnímu ss</inlineAttr> </f> </text> </region> <region region-id="4331" left="24" top="19274.25" width="107.25" height="21.75" align-x="45" align-y="19290" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">m</ml:id> <ml:apply> <ml:mult/> <ml:real>4.2894906</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="399"/> </region> <region region-id="4332" left="24" top="19304.25" width="81" height="15.75" align-x="45" align-y="19314" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="x2">J</ml:id> <ml:real>1.0344896</ml:real> </ml:define> </math> <rendering item-idref="400"/> </region> <region region-id="4353" left="24" top="19328.25" width="39.75" height="15.75" align-x="48.75" align-y="19338" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="xy2">J</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="401"/> </region> <region region-id="4354" left="174" top="19328.25" width="81" height="15.75" align-x="195" align-y="19338" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="y2">J</ml:id> <ml:real>1.7935719</ml:real> </ml:define> </math> <rendering item-idref="402"/> </region> <region region-id="4350" left="24" top="19346.25" width="124.5" height="21.75" align-x="48.75" align-y="19362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="xz2">J</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> <ml:real>1.2186605</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="403"/> </region> <region region-id="4352" left="174" top="19352.25" width="39.75" height="15.75" align-x="198.75" align-y="19362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yz2">J</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="404"/> </region> <region region-id="4351" left="288" top="19352.25" width="81" height="15.75" align-x="309" align-y="19362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="z2">J</ml:id> <ml:real>1.4614205</ml:real> </ml:define> </math> <rendering item-idref="405"/> </region> <region region-id="4375" left="24" top="19394.25" width="354.75" height="12" align-x="45" align-y="19404" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Přepočet momentů setrvačnosti k osám na momenty setrvačnosti k rovinám </text> </region> <region region-id="115" left="30" top="19420.5" width="102.75" height="31.5" align-x="54.75" align-y="19440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="xx2">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="y2">J</ml:id> <ml:id xml:space="preserve" subscript="z2">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="x2">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="406"/> </region> <region region-id="4361" left="192" top="19430.25" width="68.25" height="74.25" align-x="219" align-y="19470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t22">P</ml:id> <ml:matrix rows="4" cols="1"> <ml:id xml:space="preserve" subscript="t22">x</ml:id> <ml:id xml:space="preserve" subscript="t22">y</ml:id> <ml:id xml:space="preserve" subscript="t22">z</ml:id> <ml:real>1</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="407"/> </region> <region region-id="4362" left="300" top="19433.25" width="88.5" height="67.5" align-x="326.25" align-y="19470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t22">P</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="1"> <ml:real>-0.072368752000000008</ml:real> <ml:real>0</ml:real> <ml:real>-0.047439674</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="408"/> </region> <region region-id="119" left="30" top="19456.5" width="102.75" height="31.5" align-x="54.75" align-y="19476" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yy2">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="z2">J</ml:id> <ml:id xml:space="preserve" subscript="x2">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="y2">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="409"/> </region> <region region-id="121" left="30" top="19492.5" width="102.75" height="31.5" align-x="54.75" align-y="19512" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="zz2">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="x2">J</ml:id> <ml:id xml:space="preserve" subscript="y2">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="z2">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="410"/> </region> <region region-id="4376" left="30" top="19538.25" width="135.75" height="12" align-x="50.25" align-y="19548" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Normální matice setrvačnosti </text> </region> <region region-id="4384" left="30" top="19571.25" width="126.75" height="56.25" align-x="47.25" align-y="19602" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">J</ml:id> <ml:matrix rows="3" cols="3"> <ml:id xml:space="preserve" subscript="x2">J</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xy2">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xz2">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xy2">J</ml:id> </ml:apply> <ml:id xml:space="preserve" 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<ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="xx2">J</ml:id> <ml:id xml:space="preserve" subscript="zz2">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">l</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="2">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t22">x</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="2">l</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="2">m</ml:id> </ml:apply> 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<ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="y2">J</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">l</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="2">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t22">x</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="2">l</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="2">m</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">m</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="424"/> </region> <region region-id="1905" left="312" top="20402.25" width="57.75" height="192" align-x="324" align-y="20412" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="2">K</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>0</ml:real> <ml:real>0.22214456666777627</ml:real> <ml:real>0.88820446956187715</ml:real> <ml:real>1.9970819737411851</ml:real> <ml:real>3.5470247590837416</ml:real> <ml:real>5.5357361571256609</ml:real> <ml:real>7.9605184133456506</ml:real> <ml:real>10.818438422976984</ml:real> <ml:real>14.106503354114697</ml:real> <ml:real>17.821832551456382</ml:real> <ml:real>21.961812412232625</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="425"/> </resultFormat> </math> <rendering item-idref="426"/> </region> <region region-id="4397" left="30" top="20414.25" width="236.25" height="24" align-x="48" align-y="20424" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Důležitá je neustálá kontrola úprav výrazu jeho vyčíslením před úpravou a po úpravě </text> </region> <region region-id="1907" left="24" top="20648.25" width="551.25" height="228" align-x="24" align-y="20658" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> TRAN3 MASS =<sp count="2"/>5.9261161e+01 KILOGRAM CENTER OF GRAVITY with respect to LCS3 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="5"/>2.5740416e-03<sp count="2"/>0.0000000e+00 -3.7039760e-01<sp count="2"/>M INERTIA with respect to LCS3 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>3.3435680e+01<sp count="2"/>0.0000000e+00<sp count="2"/>1.9296398e-01 Iyx Iyy Iyz<sp count="2"/>0.0000000e+00<sp count="2"/>3.4142950e+01<sp count="2"/>0.0000000e+00 Izx Izy Izz<sp count="2"/>1.9296398e-01<sp count="2"/>0.0000000e+00<sp count="2"/>1.0075258e+00 INERTIA at CENTER OF GRAVITY with respect to LCS3 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>2.5305381e+01<sp count="2"/>0.0000000e+00<sp count="2"/>1.3646327e-01 Iyx Iyy Iyz<sp count="2"/>0.0000000e+00<sp count="2"/>2.6012259e+01<sp count="2"/>0.0000000e+00 Izx Izy Izz<sp count="2"/>1.3646327e-01<sp count="2"/>0.0000000e+00<sp count="2"/>1.0071331e+00 </text> </region> <region region-id="4415" left="24" top="20894.25" width="129" height="24" align-x="24" align-y="20904" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Článek 3</inlineAttr> </f> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">momenty k lokálnímu ss</inlineAttr> </f> </text> </region> <region region-id="4420" left="24" top="20930.25" width="107.25" height="21.75" align-x="45" align-y="20946" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:apply> <ml:mult/> <ml:real>5.9261161</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="427"/> </region> <region region-id="4419" left="24" top="20960.25" width="107.25" height="21.75" align-x="45" align-y="20976" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="x3">J</ml:id> <ml:apply> <ml:mult/> <ml:real>3.3435680</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="428"/> </region> <region region-id="4439" left="24" top="20990.25" width="84.75" height="15.75" align-x="48.75" align-y="21000" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="xy3">J</ml:id> <ml:real>0.0000000</ml:real> </ml:define> </math> <rendering item-idref="429"/> </region> <region region-id="4440" left="174" top="20984.25" width="107.25" height="21.75" align-x="195" align-y="21000" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="y3">J</ml:id> <ml:apply> <ml:mult/> <ml:real>3.4142950</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="430"/> </region> <region region-id="4436" left="24" top="21008.25" width="118.5" height="21.75" align-x="48.75" align-y="21024" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="xz3">J</ml:id> <ml:apply> <ml:mult/> <ml:real>1.9296398</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="431"/> </region> <region region-id="4438" left="174" top="21014.25" width="84.75" height="15.75" align-x="198.75" align-y="21024" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yz3">J</ml:id> <ml:real>0.0000000</ml:real> </ml:define> </math> <rendering item-idref="432"/> </region> <region region-id="4437" left="312" top="21014.25" width="81" height="15.75" align-x="333" align-y="21024" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="z3">J</ml:id> <ml:real>1.0075258</ml:real> </ml:define> </math> <rendering item-idref="433"/> </region> <region region-id="4445" left="24" top="21056.25" width="354.75" height="12" align-x="45" align-y="21066" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Přepočet momentů setrvačnosti k osám na momenty setrvačnosti k rovinám </text> </region> <region region-id="4410" left="24" top="21082.5" width="102.75" height="31.5" align-x="48.75" align-y="21102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="xx3">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="y3">J</ml:id> <ml:id xml:space="preserve" subscript="z3">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="x3">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="434"/> </region> <region region-id="4411" left="24" top="21118.5" width="102.75" height="31.5" align-x="48.75" align-y="21138" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yy3">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="z3">J</ml:id> <ml:id xml:space="preserve" subscript="x3">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="y3">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="435"/> </region> <region region-id="1908" left="192" top="21098.25" width="68.25" height="74.25" align-x="219" align-y="21138" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t33">P</ml:id> <ml:matrix rows="4" cols="1"> <ml:id xml:space="preserve" subscript="t33">x</ml:id> <ml:id xml:space="preserve" subscript="t33">y</ml:id> <ml:id xml:space="preserve" subscript="t33">z</ml:id> <ml:real>1</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="436"/> </region> <region region-id="1910" left="294" top="21098.25" width="118.5" height="73.5" align-x="320.25" align-y="21138" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t33">P</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="1"> <ml:real>0.0025740416</ml:real> <ml:real>0</ml:real> <ml:real>-0.3703976</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="437"/> </region> <region region-id="4412" left="24" top="21154.5" width="102.75" height="31.5" align-x="48.75" align-y="21174" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="zz3">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="x3">J</ml:id> <ml:id xml:space="preserve" subscript="y3">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="z3">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="438"/> </region> <region region-id="4446" left="24" top="21212.25" width="135.75" height="12" align-x="44.25" align-y="21222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Normální matice setrvačnosti </text> </region> <region region-id="4449" left="24" top="21239.25" width="126.75" height="56.25" align-x="41.25" align-y="21270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">J</ml:id> <ml:matrix rows="3" cols="3"> <ml:id xml:space="preserve" subscript="x3">J</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xy3">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xz3">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xy3">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="y3">J</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="yz3">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xz3">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="yz3">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="z3">J</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="439"/> </region> <region region-id="4448" left="246" top="21242.25" width="161.25" height="49.5" align-x="262.5" align-y="21270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="3"> <ml:real>33.43568</ml:real> <ml:real>0</ml:real> <ml:real>-0.19296398</ml:real> <ml:real>0</ml:real> <ml:real>34.14295</ml:real> <ml:real>0</ml:real> <ml:real>-0.19296398</ml:real> <ml:real>0</ml:real> <ml:real>1.0075258</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="440"/> </region> <region region-id="4447" left="24" top="21320.25" width="147.75" height="12" align-x="50.25" align-y="21330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Homogenní matice setrvačnosti </text> </region> <region region-id="158" left="24" top="21342.75" width="228" height="76.5" align-x="43.5" align-y="21384" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">H</ml:id> <ml:matrix rows="4" cols="4"> <ml:id xml:space="preserve" subscript="xx3">J</ml:id> <ml:id xml:space="preserve" subscript="xy3">J</ml:id> <ml:id xml:space="preserve" subscript="xz3">J</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="t33">x</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="xy3">J</ml:id> <ml:id xml:space="preserve" subscript="yy3">J</ml:id> <ml:id xml:space="preserve" subscript="yz3">J</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="t33">y</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="xz3">J</ml:id> <ml:id xml:space="preserve" subscript="yz3">J</ml:id> <ml:id xml:space="preserve" subscript="zz3">J</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="t33">z</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="t33">x</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="t33">y</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="t33">z</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="3">m</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="441"/> </region> <region region-id="159" left="270" top="21347.25" width="186.75" height="67.5" align-x="288.75" align-y="21384" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">H</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>0.85739790000000227</ml:real> <ml:real>0</ml:real> <ml:real>0.19296398</ml:real> <ml:real>0.15254069367829762</ml:real> <ml:real>0</ml:real> <ml:real>0.15012790000000109</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.19296398</ml:real> <ml:real>0</ml:real> <ml:real>33.285552100000004</ml:real> <ml:real>-21.9501918076136</ml:real> <ml:real>0.15254069367829762</ml:real> <ml:real>0</ml:real> <ml:real>-21.9501918076136</ml:real> <ml:real>59.261161</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="442"/> </region> <region region-id="160" left="24" top="21458.25" width="195.75" height="12" align-x="24" align-y="21468" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Kinetická energie třetího článku</inlineAttr> </f> </text> </region> <region region-id="161" left="24" top="21480.75" width="183.75" height="29.25" align-x="56.25" align-y="21498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> 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xml:space="preserve">t</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>0</ml:real> <ml:real>0.83740675238908024</ml:real> <ml:real>3.3493738846883394</ml:real> <ml:real>7.5352853737020222</ml:real> <ml:real>13.394572861856371</ml:real> <ml:real>20.927336933791629</ml:real> <ml:real>30.135091556700644</ml:real> <ml:real>41.021523044489456</ml:real> <ml:real>53.593147357480753</ml:real> <ml:real>67.859757921022023</ml:real> <ml:real>83.834580654695827</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="444"/> </resultFormat> </math> <rendering item-idref="445"/> </region> <region region-id="4465" left="24" top="21704.25" width="669.75" height="12" align-x="24" align-y="21714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Pro odvození výrazu pro kinetickou energii pro ruční použití v Lagr.rov. II. druhu provedeme symbolicky roznásobení (Shift+F9) </text> </region> <region region-id="164" left="24" top="21740.25" width="1416.75" height="81" align-x="56.25" align-y="21786" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">tr</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> 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is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Po symbolickém vynásobení </text> </region> <region region-id="1016" left="24" top="21858.75" width="5332.5" height="29.25" align-x="56.25" align-y="21876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> 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<ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="2">l</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="t33">x</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="501"/> </region> <region region-id="4942" left="36" top="24110.25" width="319.5" height="12" align-x="57" align-y="24120" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výsledný upravený výraz pro kinetickou energii celého mechanismu </text> </region> <region region-id="4940" left="36" top="24138.75" width="510.75" height="29.25" align-x="63.75" align-y="24156" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> 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<ml:real>2112.4269657666896</ml:real> <ml:real>2129.4577152722641</ml:real> <ml:real>2148.4920823667294</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="510"/> </resultFormat> </math> <rendering item-idref="511"/> </region> <region region-id="5027" left="36" top="24386.25" width="405" height="12" align-x="36" align-y="24396" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> M<f family="Arial CE" charset="238"> <inlineAttr line-through="false">ísto hmotnostních parametrů pro zjednodušení použity nové konstanty</inlineAttr> </f> </text> </region> <region region-id="5038" left="36" top="24416.25" width="264" height="15.75" align-x="54.75" align-y="24426" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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</ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="512"/> </region> <region region-id="5039" left="36" top="24434.25" width="90" height="15.75" align-x="54.75" align-y="24444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">g</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="2">m</ml:id> <ml:id xml:space="preserve" subscript="3">m</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="513"/> </region> <region region-id="5079" left="36" top="24458.25" width="302.25" height="12" align-x="57" align-y="24468" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výsledný upravený výraz pro potenciální energii celého systému </text> </region> <region region-id="5044" left="36" top="24488.25" width="104.25" height="15.75" align-x="63" align-y="24498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">P</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">e</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="514"/> </region> <region region-id="5045" left="162" top="24488.25" width="70.5" height="192" align-x="171" align-y="24498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>2048.3112029221747</ml:real> <ml:real>2049.31301171662</ml:real> <ml:real>2052.3184380999569</ml:real> <ml:real>2057.3274820721845</ml:real> <ml:real>2064.3401436333033</ml:real> <ml:real>2073.3564227833135</ml:real> <ml:real>2084.3763195222145</ml:real> <ml:real>2097.3998338500064</ml:real> <ml:real>2112.42696576669</ml:real> <ml:real>2129.4577152722641</ml:real> <ml:real>2148.49208236673</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="515"/> </resultFormat> </math> <rendering item-idref="516"/> </region> <region region-id="202" left="30" top="24703.5" width="578.25" height="21" align-x="30" align-y="24720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238" size="18"> <inlineAttr line-through="false">Výpočet zobecněné síly pomocí Lagrangeovy pohybové rovnice II. druhu</inlineAttr> </f> </text> </region> <region region-id="5160" left="36" top="24744" width="144" height="46.5" align-x="36" align-y="24744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="517" display-width="142.5" display-height="45"/> </picture> <rendering item-idref="518"/> </region> <region region-id="5196" left="36" top="24812.25" width="99.75" height="12" align-x="36" align-y="24822" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Výpočet τ1</inlineAttr> </f> </text> </region> <region region-id="5195" left="36" top="24836.25" width="255" height="12" align-x="54.75" align-y="24846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výpočet prvního členu Lagr. pohybové rovnice - L11(t) </text> </region> <region region-id="5194" left="36" top="24860.25" width="345" height="12" align-x="36" align-y="24870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Parciální derivaci K(t) podle dq1(t) je třeba udělat ručně:</inlineAttr> </f> </text> </region> <region region-id="5193" left="36" top="24888.75" width="510.75" height="29.25" align-x="63.75" align-y="24906" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> 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<ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="519"/> </region> <region region-id="5192" left="36" top="24920.25" width="282.75" height="21.75" align-x="69.75" align-y="24936" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> 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<ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="520"/> </region> <region region-id="5191" left="36" top="24956.25" width="372" height="12" align-x="36" align-y="24966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Derivaci podle času provede Mathcad, je ji potřeba ale ručně upravit</inlineAttr> </f> <sp/> </text> </region> <region region-id="5190" left="36" top="24996" width="305.25" height="31.5" align-x="74.25" align-y="25014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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xml:space="preserve" subscript="0">a</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> </ml:apply> </ml:define> </math> <rendering item-idref="521"/> </region> <region region-id="5189" left="36" top="25038" width="540.75" height="31.5" align-x="74.25" align-y="25056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L11</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="522"/> </region> <region region-id="5188" left="36" top="25082.25" width="519.75" height="21.75" align-x="74.25" align-y="25098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L11</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="523"/> </region> <region region-id="5187" left="36" top="25142.25" width="218.25" height="12" align-x="36" align-y="25152" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Druhý člen Lagr. rovnice L12(t)</inlineAttr> </f> </text> </region> <region region-id="5186" left="36" top="25166.25" width="569.25" height="12" align-x="36" align-y="25176" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Mathcad neumí symbolicky, proto ručně, v kinetické energii nikde není q1(t), proto výsledek druhého členu je 0</inlineAttr> </f> </text> </region> <region region-id="5185" left="36" top="25196.25" width="53.25" height="13.5" align-x="74.25" align-y="25206" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L12</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="524"/> </region> <region region-id="5184" left="36" top="25232.25" width="200.25" height="12" align-x="36" align-y="25242" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Třetí člen L13(t)</inlineAttr> </f> </text> </region> <region region-id="5183" left="36" top="25262.25" width="104.25" height="15.75" align-x="63" align-y="25272" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">P</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">e</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="525"/> </region> <region region-id="5182" left="36" top="25290" width="108" height="33.75" align-x="36" align-y="25308" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:boundVars> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">e</ml:id> </ml:apply> </ml:parens> </ml:lambda> </ml:apply> </math> <rendering item-idref="526"/> </region> <region region-id="5181" left="36" top="25334.25" width="109.5" height="12" align-x="36" align-y="25344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> roven také nule </text> </region> <region region-id="5198" left="36" top="25370.25" width="264" height="12" align-x="57" align-y="25380" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výsledná zobecněná síla τ1 je tedy rovna prvnímu členu </text> </region> <region region-id="5180" left="36" top="25412.25" width="513" height="21.75" align-x="67.5" align-y="25428" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="527"/> </region> <region region-id="5200" left="36" top="25472.25" width="426.75" height="12" align-x="60" align-y="25482" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Porovnání s výsledkem získaným z Newton-Eulerových vztahů (bez vlivu vnitřních převodů) </text> </region> <region region-id="777" left="36" top="25500" width="394.5" height="307.5" align-x="36" align-y="25500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="528"/> <rendering item-idref="529"/> </region> <region region-id="1920" left="504" top="25500" width="421.5" height="295.5" align-x="504" align-y="25500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="530"/> <rendering item-idref="531"/> </region> <region region-id="5335" left="30" top="25874.25" width="240.75" height="12" align-x="30" align-y="25884" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Druhá zobecněná síla τ2, první člen L21(t) </text> </region> <region region-id="5324" left="30" top="25904.25" width="246" height="12" align-x="30" align-y="25914" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Kinetická energie po ruční derivaci podle dq2 </text> </region> <region region-id="5325" left="30" top="25926.75" width="510.75" height="29.25" align-x="57.75" align-y="25944" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="532"/> </region> <region region-id="5326" left="30" top="25976.25" width="51" height="15.75" align-x="63.75" align-y="25986" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> </ml:apply> </math> <rendering item-idref="533"/> </region> <region region-id="5327" left="30" top="25998" width="115.5" height="31.5" align-x="68.25" align-y="26016" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L21</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> </ml:apply> </ml:parens> </ml:lambda> </ml:apply> </ml:define> </math> <rendering item-idref="534"/> </region> <region region-id="5328" left="30" top="26042.25" width="103.5" height="15.75" align-x="68.25" align-y="26052" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L21</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="535"/> </region> <region region-id="5329" left="30" top="26084.25" width="386.25" height="12" align-x="30" align-y="26094" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">druhý člen L22(t) roven nule - v kinetické energii není nikde q2(t)</inlineAttr> </f> </text> </region> <region region-id="5330" left="30" top="26112" width="108" height="33.75" align-x="30" align-y="26130" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:boundVars> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">e</ml:id> </ml:apply> </ml:parens> </ml:lambda> </ml:apply> </math> <rendering item-idref="536"/> </region> <region region-id="5205" left="30" top="26162.25" width="280.5" height="12" align-x="30" align-y="26172" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">třetí člen L23(t) - derivace potenciální energie podle q2(t)</inlineAttr> </f> </text> </region> <region region-id="5339" left="30" top="26186.25" width="104.25" height="15.75" align-x="57" align-y="26196" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">P</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">e</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="537"/> </region> <region region-id="5331" left="30" top="26210.25" width="58.5" height="15.75" align-x="68.25" align-y="26220" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L23</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:id xml:space="preserve" subscript="1">e</ml:id> </ml:define> </math> <rendering item-idref="538"/> </region> <region region-id="5332" left="30" top="26240.25" width="158.25" height="12" align-x="30" align-y="26250" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Druhá zobecnìná síla </text> </region> <region region-id="5333" left="30" top="26264.25" width="120.75" height="15.75" align-x="61.5" align-y="26274" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="2">τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="1">e</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="539"/> </region> <region region-id="5347" left="30" top="26336.25" width="426.75" height="12" align-x="54" align-y="26346" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Porovnání s výsledkem získaným z Newton-Eulerových vztahů (bez vlivu vnitřních převodů) </text> </region> <region region-id="1921" left="6" top="26364" width="438" height="286.5" align-x="6" align-y="26364" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="540"/> <rendering item-idref="541"/> </region> <region region-id="1923" left="492" top="26370" width="429" height="280.5" align-x="492" align-y="26370" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="542"/> <rendering item-idref="543"/> </region> <region region-id="5379" left="30" top="26726.25" width="455.25" height="12" align-x="30" align-y="26736" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Třetí zob síla, první člen L31(t), derivace K(t) ručně derivaci podle dq3(t) a pak podle času</inlineAttr> </f> </text> </region> <region region-id="5378" left="30" top="26766.75" width="510.75" height="29.25" align-x="57.75" align-y="26784" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="544"/> </region> <region region-id="5377" left="30" top="26804.25" width="132" height="12" align-x="50.25" align-y="26814" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Derivace ručně podle dq3(t) </text> </region> <region region-id="5376" left="30" top="26828.25" width="113.25" height="15.75" align-x="85.5" align-y="26838" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="545"/> </region> <region region-id="5375" left="30" top="26852.25" width="96" height="12" align-x="50.25" align-y="26862" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Derivace podle času </text> </region> <region region-id="5374" left="30" top="26868" width="131.25" height="31.5" align-x="30" align-y="26886" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> </ml:apply> </math> <rendering item-idref="546"/> </region> <region region-id="5373" left="30" top="26910" width="134.25" height="31.5" align-x="96" align-y="26928" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="547"/> </region> <region region-id="5372" left="30" top="26960.25" width="171.75" height="15.75" align-x="68.25" align-y="26970" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L31</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="548"/> </region> <region region-id="5371" left="30" top="27032.25" width="240.75" height="12" align-x="30" align-y="27042" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">druhý člen L32(t) , parciálně K(t) podle q3(t)</inlineAttr> </f> </text> </region> <region region-id="5370" left="30" top="27060.75" width="175.5" height="29.25" align-x="109.5" align-y="27078" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="1">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="549"/> </region> <region region-id="5369" left="30" top="27096.75" width="200.25" height="29.25" align-x="68.25" align-y="27114" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L32</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="550"/> </region> <region region-id="5368" left="30" top="27134.25" width="345" height="12" align-x="30" align-y="27144" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">třetí člen L33(t) derivace P(t) podle q3(t) - nikde není, roven nule</inlineAttr> </f> </text> </region> <region region-id="5367" left="30" top="27162" width="108" height="33.75" align-x="30" align-y="27180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:boundVars> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">e</ml:id> </ml:apply> </ml:parens> </ml:lambda> </ml:apply> </math> <rendering item-idref="551"/> </region> <region region-id="5366" left="30" top="27240.75" width="330.75" height="29.25" align-x="61.5" align-y="27258" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="552"/> </region> <region region-id="5365" left="408" top="27248.25" width="340.5" height="12" align-x="408" align-y="27258" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> První člen je zrychlující síla, druhý tečná, třetí odstředivá síla </text> </region> <region region-id="5382" left="30" top="27314.25" width="426.75" height="12" align-x="54" align-y="27324" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Porovnání s výsledkem získaným z Newton-Eulerových vztahů (bez vlivu vnitřních převodů) </text> </region> <region region-id="801" left="6" top="27342" width="364.5" height="331.5" align-x="6" align-y="27342" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="553"/> <rendering item-idref="554"/> </region> <region region-id="1925" left="468" top="27348" width="391.5" height="331.5" align-x="468" align-y="27348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="555"/> <rendering item-idref="556"/> </region> <region region-id="5509" left="36" top="27722.25" width="304.5" height="12" align-x="57" align-y="27732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výsledné Lagrangeovy pohybové rovnice - bez vnitřních převodů </text> </region> <region region-id="5495" left="36" top="27758.25" width="474" height="21.75" align-x="67.5" align-y="27774" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> 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xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="2">τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="1">e</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="558"/> </region> <region region-id="5497" left="36" top="27828.75" width="330.75" height="29.25" align-x="67.5" align-y="27846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="559"/> </region> <region region-id="5498" left="36" top="27883.5" width="601.5" height="42" align-x="36" align-y="27900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238" size="18"> <inlineAttr line-through="false">Zahrnutí vlivu vnitřních převodů a rozvodů na dynamiku mechanismu (redukované momenty a hmotnosti)</inlineAttr> </f> </text> </region> <region region-id="5524" left="36" top="27962.25" width="100.5" height="15.75" align-x="58.5" align-y="27972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="p1">J</ml:id> <ml:real>5.8702800000</ml:real> </ml:define> </math> <rendering item-idref="560"/> </region> <region region-id="5525" left="210" top="27962.25" width="577.5" height="12" align-x="210" align-y="27972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Zahrnutí vlivu momentu setrvačnosti rotoru motoru, převodovky a vnitřních kroužků velkých ložisek</inlineAttr> </f> </text> </region> <region region-id="5526" left="36" top="27986.25" width="87.75" height="15.75" align-x="63.75" align-y="27996" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math 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<ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="p12">m</ml:id> <ml:id xml:space="preserve" subscript="p21">J</ml:id> </ml:define> </math> <rendering item-idref="562"/> </region> <region region-id="5515" left="210" top="28010.25" width="420" height="12" align-x="210" align-y="28020" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Zahrnutí vlivu zrychlení ROT1 na vnitřní převody TRAN2</inlineAttr> </f> </text> </region> <region region-id="5516" left="36" top="28034.25" width="104.25" height="15.75" align-x="62.25" align-y="28044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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<ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="p3">m</ml:id> <ml:real>51.5751826083</ml:real> </ml:define> </math> <rendering item-idref="564"/> </region> <region region-id="5523" left="210" top="28058.25" width="747.75" height="12" align-x="210" align-y="28068" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Zahrnutí zvýšení redukované hmotnosti vlivem zrychlení rotoru motoru MOT3, ozubeného kola a matice pohybového šroubu (řemen neuvažován)</inlineAttr> </f> </text> </region> <region region-id="5532" left="36" top="28088.25" width="249.75" height="12" align-x="36" align-y="28098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Pozn. - Nejsou uvažovány gyroskopické efekty </text> </region> <region region-id="5549" left="36" top="28154.25" width="579.75" height="21.75" align-x="67.5" align-y="28170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> 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background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Zavedení nových koeficientů - zahrnují hmotnostní parametry a polohy těžišť </text> </region> <region region-id="5584" left="36" top="28298.25" width="66.75" height="15.75" align-x="54.75" align-y="28308" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="0">a</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="0">a</ml:id> <ml:id xml:space="preserve" subscript="p1">J</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="568"/> </region> <region region-id="5585" left="36" top="28322.25" width="70.5" height="15.75" align-x="54.75" align-y="28332" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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subscript="1">e</ml:id> <ml:real>0</ml:real> </ml:matrix> </ml:apply> </ml:parens> </ml:define> </math> <rendering item-idref="597"/> </region> <region region-id="5669" left="42" top="29509.5" width="548.25" height="75.75" align-x="70.5" align-y="29550" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">Τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id 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xml:space="preserve" subscript="2">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="1">e</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="0">c</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="1">a</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="598"/> </region> <region region-id="5673" left="42" top="29606.25" width="516.75" height="12" align-x="60" align-y="29616" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Opačná úloha - zjištění počátečního vektoru zrychlení DDQ(t)<sp count="2"/>při buzení známým průběhem zobecněných sil </text> </region> <region region-id="5671" left="42" top="29654.25" width="771.75" height="70.5" align-x="85.5" align-y="29694" show-border="false" 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</ml:apply> </ml:matrix> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:real>0</ml:real> </ml:matrix> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:matrix rows="3" cols="3"> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="0">f</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="0">f</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:matrix> <ml:real>-1</ml:real> </ml:apply> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:id xml:space="preserve" subscript="1">τ</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="2">τ</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">τ</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:matrix> </ml:apply> </ml:apply> </ml:parens> </ml:define> </math> <rendering item-idref="599"/> </region> <region region-id="1327" left="90" top="29808" width="190.5" height="157.5" align-x="90" align-y="29808" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="600"/> <rendering item-idref="601"/> </region> <region region-id="1328" left="462" top="29808" width="175.5" height="157.5" align-x="462" align-y="29808" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="602"/> <rendering item-idref="603"/> </region> <region region-id="1366" left="330" top="29858.25" width="143.25" height="24" align-x="341.25" align-y="29868" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">stejné jako požadované zrychlení</inlineAttr> </f> </text> </region> </regions> <binaryContent> <item item-id="1" 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xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="b3">T</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="b0">A</ml:id> <ml:id xml:space="preserve" subscript="01">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="12">A</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="44"/> </region> <region region-id="2079" left="36" top="1994.25" width="578.25" height="12" align-x="43.5" align-y="2004" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Pro sestavení rovnic inverzní úlohy je celková transformační matice vyjádřena symbolickým vynásobením jednotlivých matic </text> </region> <region region-id="1452" left="36" top="2031" width="390.75" height="72" align-x="60.75" align-y="2070" 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<ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-0.064999999999999877</ml:real> <ml:real>1.01</ml:real> <ml:real>1.454</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="88"/> </region> <region region-id="2110" left="42" top="4052.25" width="451.5" height="12" align-x="42" align-y="4062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Kontrola správnosti sestavení transformačních matic s průběhem konc. bodu (poč. 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<ml:real>-0.11400000000000019</ml:real> <ml:real>-0.12900000000000023</ml:real> <ml:real>-0.14599999999999991</ml:real> <ml:real>-0.16500000000000023</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="89"/> </resultFormat> </math> <rendering item-idref="90"/> </region> <region region-id="2115" left="126" top="4106.25" width="55.5" height="192" align-x="134.25" align-y="4116" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>-0.065</ml:real> <ml:real>-0.066</ml:real> <ml:real>-0.069</ml:real> <ml:real>-0.074</ml:real> <ml:real>-0.081</ml:real> <ml:real>-0.090000000000000011</ml:real> <ml:real>-0.101</ml:real> <ml:real>-0.11400000000000002</ml:real> <ml:real>-0.129</ml:real> <ml:real>-0.146</ml:real> <ml:real>-0.16500000000000004</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="91"/> </resultFormat> </math> <rendering item-idref="92"/> </region> <region region-id="2114" left="210" top="4106.25" width="52.5" height="198" align-x="232.5" align-y="4116" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:apply> <ml:id xml:space="preserve" subscript="b3">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:sequence> <ml:real>2</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> 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<ml:real>1.011</ml:real> <ml:real>1.014</ml:real> <ml:real>1.019</ml:real> <ml:real>1.026</ml:real> <ml:real>1.035</ml:real> <ml:real>1.046</ml:real> <ml:real>1.059</ml:real> <ml:real>1.074</ml:real> <ml:real>1.091</ml:real> <ml:real>1.11</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="95"/> </resultFormat> </math> <rendering item-idref="96"/> </region> <region region-id="2112" left="360" top="4106.25" width="52.5" height="198" align-x="382.5" align-y="4116" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:apply> <ml:id xml:space="preserve" subscript="b3">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:sequence> <ml:real>3</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> <result 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<result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>1.454</ml:real> <ml:real>1.4549999999999999</ml:real> <ml:real>1.458</ml:real> <ml:real>1.4629999999999999</ml:real> <ml:real>1.47</ml:real> <ml:real>1.4789999999999999</ml:real> <ml:real>1.49</ml:real> <ml:real>1.503</ml:real> <ml:real>1.518</ml:real> <ml:real>1.535</ml:real> <ml:real>1.554</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="99"/> </resultFormat> </math> <rendering item-idref="100"/> </region> <region region-id="2119" left="42" top="4382.25" width="219" height="12" align-x="42" align-y="4392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Výpočet dalších kinematických veličin</inlineAttr> </f> </text> </region> <region region-id="2118" left="42" top="4418.25" width="120.75" height="12" align-x="42" align-y="4428" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> vektory na osách z </text> </region> <region region-id="2230" left="48" top="4448.25" width="158.25" height="15.75" align-x="78.75" align-y="4458" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="0">k</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">submatrix</ml:id> <ml:sequence> <ml:id xml:space="preserve" subscript="b0">T</ml:id> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>3</ml:real> <ml:real>3</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="101"/> </region> <region region-id="2221" left="228" top="4448.25" width="171" height="15.75" align-x="258.75" align-y="4458" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">k</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">submatrix</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve" subscript="b1">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>3</ml:real> <ml:real>3</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="102"/> </region> <region region-id="2219" left="420" top="4448.25" width="171" height="15.75" align-x="450.75" align-y="4458" 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xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">k</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">submatrix</ml:id> <ml:sequence> <ml:apply> <ml:id xml:space="preserve" subscript="b3">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>3</ml:real> <ml:real>3</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="104"/> </region> <region region-id="2229" left="48" top="4478.25" width="60" height="49.5" align-x="78.75" align-y="4506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="0">k</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="105"/> </region> <region region-id="2182" left="228" top="4478.25" width="60" height="49.5" align-x="258.75" align-y="4506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">k</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="106"/> </region> <region region-id="2218" left="420" top="4476" width="108.75" height="54" align-x="450.75" align-y="4506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="2">k</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="107"/> </region> <region region-id="2214" left="618" top="4476" width="108.75" height="54" align-x="648.75" align-y="4506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">k</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="108"/> </region> <region region-id="2228" left="48" top="4538.25" width="68.25" height="49.5" align-x="81" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="0">k</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="109"/> </region> <region region-id="2178" left="228" top="4538.25" width="68.25" height="49.5" align-x="261" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="1">k</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="110"/> </region> <region region-id="2217" left="420" top="4538.25" width="68.25" height="49.5" align-x="453" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="2">k</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>1.2246063538223773E-16</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="111"/> </region> <region region-id="2176" left="618" top="4538.25" width="68.25" height="49.5" align-x="651" align-y="4566" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="3">k</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>1.2246063538223773E-16</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="112"/> </region> <region region-id="2245" left="48" top="4616.25" width="159" height="12" align-x="48" align-y="4626" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Submatice rotace </text> </region> <region region-id="2244" left="48" top="4652.25" width="153" height="15.75" align-x="73.5" align-y="4662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="b0">R</ml:id> <ml:apply> <ml:id xml:space="preserve">submatrix</ml:id> <ml:sequence> <ml:id xml:space="preserve" subscript="b0">T</ml:id> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>1</ml:real> <ml:real>3</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="113"/> </region> <region region-id="2220" left="228" top="4652.25" width="178.5" height="15.75" align-x="266.25" align-y="4662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Vektor do koncového bodu </text> </region> <region region-id="2481" left="48" top="5366.25" width="207" height="15.75" align-x="84.75" align-y="5376" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="03">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">submatrix</ml:id> <ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve" subscript="b3">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="b0">T</ml:id> </ml:apply> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>4</ml:real> <ml:real>4</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="142"/> </region> <region region-id="2482" left="48" top="5414.25" width="162.75" height="12" align-x="48" align-y="5424" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Rychlost článku 0 - podstavce</inlineAttr> </f> </text> </region> <region region-id="2483" left="48" top="5438.25" width="60" height="49.5" align-x="78.75" align-y="5466" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="0">v</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="143"/> </region> <region region-id="2903" left="48" top="5510.25" width="228.75" height="12" align-x="48" align-y="5520" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Vzájemné rychlosti ručně zjednodušeně</inlineAttr> </f> </text> </region> <region region-id="2931" left="48" top="5528.25" width="65.25" height="49.5" align-x="84" align-y="5556" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="01">v</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> 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<text use-page-width="false" push-down="false" lock-width="true"> v zákl. ss. </text> </region> <region region-id="2925" left="48" top="5582.25" width="82.5" height="49.5" align-x="95.25" align-y="5610" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="01">v</ml:id> <ml:real>0.1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="147"/> </region> <region region-id="2926" left="348" top="5582.25" width="91.5" height="49.5" align-x="395.25" align-y="5610" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="12">v</ml:id> <ml:real>0.1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.49999999999999434</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="148"/> </region> <region region-id="2927" left="690" top="5582.25" width="109.5" height="49.5" align-x="737.25" align-y="5610" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="23">v</ml:id> <ml:real>0.1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>-0.013090080263343719</ml:real> <ml:real>0.54233999302057734</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="149"/> </region> <region region-id="2900" left="48" top="5666.25" width="746.25" height="12" align-x="48" align-y="5676" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Vzájemné rychlosti univerzální obecný tvar - vystupuje zde parciální derivace vektoru p podle kloubové proměnné q - pomocí diferenciálních operátorů</inlineAttr> </f> </text> </region> <region region-id="2920" left="54" top="5699.25" width="96.75" height="67.5" align-x="72.75" align-y="5736" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" 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background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="23">v</ml:id> <ml:real>0.1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>-0.013090080263343719</ml:real> <ml:real>0.54233999302057734</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="157"/> </region> <region region-id="2934" left="48" top="5906.25" width="849.75" height="12" align-x="75.75" align-y="5916" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Alternativně nejprve derivace vektoru p23 v lokálním souřadném systému, výsledkem je vektor rychlosti v lokálním ss., ten se vyjádří v základním ss. jen násobením submaticí rotace </text> </region> <region region-id="2933" left="48" top="5936.25" width="275.25" height="15.75" align-x="84" align-y="5946" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="23">v</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="b2">R</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">submatrix</ml:id> <ml:sequence> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="t">D</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="23">A</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> <ml:real>3</ml:real> 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<ml:function> <ml:id xml:space="preserve" subscript="01">ε</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="0">k</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="182"/> </region> <region region-id="2955" left="252" top="6524.25" width="65.25" height="49.5" align-x="288" align-y="6552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="12">ε</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> 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disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">ε</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="0">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="185"/> </region> <region region-id="905" left="42" top="6620.25" width="184.5" height="15.75" align-x="72.75" align-y="6630" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="2">ε</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="12">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="12">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="186"/> </region> <region region-id="2957" left="42" top="6644.25" width="184.5" height="15.75" align-x="72.75" align-y="6654" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">ε</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="23">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="23">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="187"/> </region> <region region-id="2966" left="42" top="6692.25" width="465" height="12" align-x="42" align-y="6702" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Výpočet relativních translačních zrychlení počátků lokálních souřadných systémů</inlineAttr> </f> </text> </region> <region region-id="3010" left="42" top="6728.25" width="60.75" height="49.5" align-x="73.5" align-y="6756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="0">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="188"/> </region> <region region-id="3021" left="192" top="6746.25" width="250.5" height="12" align-x="216.75" align-y="6756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Translační zrychlení pošátku lokálního ss. podstavce </text> </region> <region region-id="3023" left="42" top="6806.25" width="248.25" height="15.75" align-x="78.75" align-y="6816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="01">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="01">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="01">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="01">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="189"/> </region> <region region-id="3022" left="390" top="6806.25" width="107.25" height="12" align-x="390" align-y="6816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Pro rotační</inlineAttr> </f> </text> </region> <region region-id="3026" left="42" top="6866.25" width="114" height="15.75" align-x="78.75" align-y="6876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="12">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">k</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="2">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="190"/> </region> <region region-id="3025" left="198" top="6847.5" width="96" height="51.75" align-x="234.75" align-y="6876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="12">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:id xml:space="preserve" subscript="2">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="191"/> </region> <region region-id="3024" left="390" top="6866.25" width="105.75" height="12" align-x="390" align-y="6876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Translační</inlineAttr> </f> </text> </region> <region region-id="3033" left="42" top="6932.25" width="114" height="15.75" align-x="78.75" align-y="6942" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="23">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="2">k</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="192"/> </region> <region region-id="3034" left="198" top="6912" width="159.75" height="54" align-x="234.75" align-y="6942" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="23">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="193"/> </region> <region region-id="3035" left="390" top="6932.25" width="88.5" height="12" align-x="390" align-y="6942" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Translační</inlineAttr> </f> </text> </region> <region region-id="3037" left="42" top="6998.25" width="332.25" height="12" align-x="60.75" align-y="7008" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výpočet translačních zrychlení počátků lokálních souřadných systémů </text> </region> <region region-id="920" left="42" top="7040.25" width="406.5" height="15.75" align-x="73.5" align-y="7050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="0">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:parens> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">v</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="0">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="01">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="194"/> </region> <region region-id="921" left="42" top="7070.25" width="406.5" height="15.75" align-x="73.5" align-y="7080" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="12">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="12">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:parens> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="12">v</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="12">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="195"/> </region> <region region-id="922" left="42" top="7100.25" width="406.5" height="15.75" align-x="73.5" align-y="7110" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">a</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="23">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ε</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="23">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:parens> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="23">v</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:crossProduct/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="23">p</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="196"/> </region> <region region-id="3046" left="42" top="7142.25" width="493.5" height="12" align-x="42" align-y="7152" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Kontrola zrychlení - odpovídá zadání ax, ay a az - definice pohybu konc. bodu na začátku výpočtu </text> </region> <region region-id="3346" left="168" top="7190.25" width="47.25" height="192" align-x="168.75" align-y="7200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">t</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>0</ml:real> <ml:real>0.02</ml:real> <ml:real>0.04</ml:real> <ml:real>0.06</ml:real> <ml:real>0.08</ml:real> <ml:real>0.1</ml:real> <ml:real>0.12</ml:real> <ml:real>0.14</ml:real> <ml:real>0.16</ml:real> <ml:real>0.18</ml:real> <ml:real>0.2</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="197"/> </resultFormat> </math> <rendering item-idref="198"/> </region> <region region-id="3347" left="216" top="7190.25" width="41.25" height="198" align-x="235.5" align-y="7200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:apply> <ml:id xml:space="preserve" subscript="3">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>-4.999999999891422</ml:real> <ml:real>-5.0000000000921769</ml:real> <ml:real>-4.9999999999007212</ml:real> <ml:real>-5.0000000000463842</ml:real> <ml:real>-4.9999999999707541</ml:real> <ml:real>-5.0000000000230775</ml:real> <ml:real>-5.0000000000181695</ml:real> <ml:real>-5.0000000000260219</ml:real> <ml:real>-5.000000000034694</ml:real> <ml:real>-5.0000000000177716</ml:real> <ml:real>-4.9999999999848654</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="199"/> </resultFormat> </math> <rendering item-idref="200"/> </region> <region region-id="3348" left="288" top="7190.25" width="41.25" height="198" align-x="307.5" align-y="7200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:apply> <ml:id xml:space="preserve" subscript="3">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:sequence> <ml:real>2</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>4.9999999997850155</ml:real> <ml:real>4.999999999467458</ml:real> <ml:real>5.0000000000728679</ml:real> <ml:real>4.9999999999808518</ml:real> <ml:real>5.0000000001221592</ml:real> <ml:real>4.9999999999883524</ml:real> <ml:real>5.00000000000407</ml:real> <ml:real>4.9999999999764455</ml:real> <ml:real>5.0000000000196021</ml:real> <ml:real>4.9999999999824629</ml:real> <ml:real>5.000000000006688</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="201"/> </resultFormat> </math> <rendering item-idref="202"/> </region> <region region-id="3349" left="366" top="7190.25" width="41.25" height="198" align-x="385.5" align-y="7200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:apply> <ml:id xml:space="preserve" subscript="3">a</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:sequence> <ml:real>3</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>5.000000000007577</ml:real> <ml:real>5.0000000001619131</ml:real> <ml:real>5.0000000000171063</ml:real> <ml:real>4.9999999999998659</ml:real> <ml:real>5.0000000000006395</ml:real> <ml:real>5.0000000000003268</ml:real> <ml:real>4.9999999999994484</ml:real> <ml:real>5.0000000000007754</ml:real> <ml:real>5.0000000000005711</ml:real> <ml:real>5.0000000000001377</ml:real> <ml:real>5.0000000000001616</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="203"/> </resultFormat> </math> <rendering item-idref="204"/> </region> <region region-id="3053" left="42" top="7190.25" width="75" height="49.5" align-x="75.75" align-y="7218" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="3">a</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="1"> <ml:real>-4.999999999891422</ml:real> <ml:real>4.9999999997850155</ml:real> <ml:real>5.000000000007577</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="205"/> </region> <region region-id="3352" left="42" top="7400.25" width="636.75" height="36" align-x="55.5" align-y="7410" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Tento úkon kontroly je velmi důležitý, pohyb koncového bodu byl řešením inverzní úlohy rozložen do jednotlivých kloubů, byly vypočteny průběhy rychlostí a zrychlení (translační i rotační) a ve zrychlení a3 se všechny veličiny skládají. Pokud tato veličina je shodná se zadáním, je jistota správnosti výpočtu až po toto místo řešení </text> </region> <region region-id="3406" left="42" top="7484.25" width="129" height="12" align-x="42" align-y="7494" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Poloha težišť z Pro/E</inlineAttr> </f> </text> </region> <region region-id="3708" left="42" top="7514.25" width="303" height="24" align-x="42" align-y="7524" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> CENTER OF GRAVITY with respect to LCS1 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="4"/>-4.0325987e-02 -1.8024766e-06<sp count="2"/>7.3574162e-01<sp count="2"/>M </text> </region> <region region-id="3704" left="384" top="7514.25" width="304.5" height="24" align-x="384" align-y="7524" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> CENTER OF GRAVITY with respect to LCS2 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="4"/>-7.2368752e-02<sp count="2"/>0.0000000e+00 -4.7439674e-02<sp count="2"/>M </text> </region> <region region-id="3701" left="732" top="7514.25" width="314.25" height="24" align-x="732" align-y="7524" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> CENTER OF GRAVITY with respect to LCS3 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="5"/>2.5740416e-03<sp count="2"/>0.0000000e+00 -3.7039760e-01<sp count="2"/>M </text> </region> <region region-id="3711" left="42" top="7562.25" width="124.5" height="21.75" align-x="66.75" align-y="7578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t11">x</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> <ml:real>4.0325987</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="206"/> </region> <region region-id="3710" left="384" top="7562.25" width="124.5" height="21.75" align-x="408.75" align-y="7578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t22">x</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> 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optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t11">y</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> <ml:real>1.8024766</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-6</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="209"/> </region> <region region-id="3713" left="384" top="7592.25" width="85.5" height="15.75" align-x="409.5" align-y="7602" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t22">y</ml:id> <ml:real>0.0000000</ml:real> </ml:define> </math> <rendering item-idref="210"/> </region> <region region-id="3712" left="732" top="7592.25" width="103.5" height="15.75" align-x="757.5" align-y="7602" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t33">y</ml:id> <ml:real>0.0000000000</ml:real> </ml:define> </math> <rendering item-idref="211"/> </region> <region region-id="3717" left="42" top="7610.25" width="118.5" height="21.75" align-x="66.75" align-y="7626" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t11">z</ml:id> <ml:apply> <ml:mult/> <ml:real>7.3574162</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="212"/> </region> <region region-id="3716" left="384" top="7610.25" width="124.5" height="21.75" align-x="408.75" align-y="7626" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t22">z</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> <ml:real>4.7439674</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="213"/> </region> <region region-id="3715" left="732" top="7610.25" width="124.5" height="21.75" align-x="756.75" align-y="7626" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t33">z</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> <ml:real>3.7039760</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="214"/> </region> <region region-id="973" left="30" top="7688.25" width="152.25" height="12" align-x="30" align-y="7698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">vektory do těžiště v lokálních ss</inlineAttr> </f> </text> </region> <region region-id="3735" left="210" top="7667.25" width="67.5" height="56.25" align-x="236.25" align-y="7698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t11">p</ml:id> <ml:matrix rows="3" cols="1"> <ml:id xml:space="preserve" subscript="t11">x</ml:id> <ml:id xml:space="preserve" subscript="t11">y</ml:id> <ml:id xml:space="preserve" subscript="t11">z</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="215"/> </region> <region region-id="3729" left="306" top="7667.25" width="67.5" height="56.25" align-x="332.25" align-y="7698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t22">p</ml:id> <ml:matrix rows="3" cols="1"> <ml:id xml:space="preserve" subscript="t22">x</ml:id> <ml:id xml:space="preserve" subscript="t22">y</ml:id> <ml:id xml:space="preserve" subscript="t22">z</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="216"/> </region> <region region-id="3730" left="402" top="7667.25" width="67.5" height="56.25" align-x="428.25" align-y="7698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t33">p</ml:id> <ml:matrix rows="3" cols="1"> <ml:id xml:space="preserve" subscript="t33">x</ml:id> <ml:id xml:space="preserve" subscript="t33">y</ml:id> <ml:id xml:space="preserve" subscript="t33">z</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="217"/> </region> <region region-id="3749" left="30" top="7760.25" width="156.75" height="24" align-x="30" align-y="7770" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">je nutno přepočítat do základního ss</inlineAttr> </f> </text> </region> <region region-id="3736" left="210" top="7760.25" width="106.5" height="15.75" align-x="249" align-y="7770" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="t1b">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="b1">R</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t11">p</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="218"/> </region> <region region-id="3737" left="210" top="7784.25" width="106.5" height="15.75" align-x="249" align-y="7794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="t2b">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="b2">R</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t22">p</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="219"/> </region> <region region-id="3738" left="210" top="7808.25" width="106.5" height="15.75" align-x="249" align-y="7818" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="t3b">p</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" 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z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> MASS =<sp count="2"/>4.8824683e+01 KILOGRAM CENTER OF GRAVITY with respect to LCS1 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="4"/>-4.0325987e-02 -1.8024766e-06<sp count="2"/>7.3574162e-01<sp count="2"/>M INERTIA with respect to LCS1 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>4.6443693e+01 -7.9670815e-06<sp count="2"/>2.0478701e+00 Iyx Iyy Iyz -7.9670815e-06<sp count="2"/>4.7356949e+01<sp count="2"/>1.4573962e-04 Izx Izy Izz<sp count="2"/>2.0478701e+00<sp count="2"/>1.4573962e-04<sp count="2"/>1.4139746e+00 INERTIA at CENTER OF GRAVITY with respect to LCS1 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>2.0014124e+01 -4.4181788e-06<sp count="2"/>5.9926583e-01 Iyx Iyy Iyz -4.4181788e-06<sp count="2"/>2.0847982e+01<sp count="2"/>8.0990420e-05 Izx Izy Izz<sp count="2"/>5.9926583e-01<sp count="2"/>8.0990420e-05<sp count="2"/>1.3345766e+00 </text> </region> <region region-id="3928" left="30" top="9224.25" width="393" height="12" align-x="30" align-y="9234" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Článek ROT1 - matice setrvačnosti k těžišti, vyjádřeno (orientace) podle LCS1</inlineAttr> </f> </text> </region> <region region-id="3929" left="30" top="9254.25" width="105" height="15.75" align-x="51" align-y="9264" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">m</ml:id> <ml:real>48.8246830000</ml:real> </ml:define> </math> <rendering 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show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="1">J</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="3"> <ml:real>20.014124</ml:real> <ml:real>4.4181788001021146E-06</ml:real> <ml:real>0.59926583000000011</ml:real> <ml:real>4.4181788001021146E-06</ml:real> <ml:real>20.847982</ml:real> <ml:real>8.0990419999926624E-05</ml:real> <ml:real>0.59926583000000011</ml:real> <ml:real>8.0990419999926624E-05</ml:real> <ml:real>1.3345766</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="255"/> </region> <region region-id="1662" left="36" top="9606" width="205.5" height="166.5" align-x="36" align-y="9606" show-border="false" show-highlight="false" is-protected="true" 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width="159" height="49.5" align-x="236.25" align-y="10368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="2">J</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="3"> <ml:real>0.93795366</ml:real> <ml:real>0.025398594000000038</ml:real> <ml:real>0</ml:real> <ml:real>0.025398594000000038</ml:real> <ml:real>1.2367697</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1.4723852</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="268"/> </region> <region region-id="1677" left="36" top="10446" width="341.25" height="165" align-x="36" align-y="10446" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <metafile mapping-mode="8" x-extent="339.7606" y-extent="163.5024" item-idref="269"/> </picture> <rendering item-idref="270"/> </region> <region region-id="4031" left="36" top="10628.25" width="507" height="240" align-x="36" align-y="10638" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> TRAN3 MASS =<sp count="2"/>5.9261161e+01 KILOGRAM CENTER OF GRAVITY with respect to LCS3 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="5"/>2.5740416e-03<sp count="2"/>0.0000000e+00 -3.7039760e-01<sp count="2"/>M INERTIA with respect to LCS3 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>3.3435680e+01<sp count="2"/>0.0000000e+00<sp count="2"/>1.9296398e-01 Iyx Iyy Iyz<sp count="2"/>0.0000000e+00<sp count="2"/>3.4142950e+01<sp count="2"/>0.0000000e+00 Izx Izy 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background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Prorotační kloub</inlineAttr> </f> </text> </region> <region region-id="4215" left="126" top="16589.25" width="96.75" height="67.5" align-x="144.75" align-y="16626" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="r">D</ml:id> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> 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<ml:matrix rows="4" cols="4"> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="0">l</ml:id> <ml:real>1</ml:real> </ml:matrix> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="371"/> </region> <region region-id="72" left="24" top="16821" width="288" height="72" align-x="67.5" align-y="16860" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="b1">dT</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="372"/> </region> <region region-id="4227" left="24" top="16940.25" width="412.5" height="12" align-x="42.75" align-y="16950" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Výpočet totálního diferenciálu (analogie derivace) transformační matice Tb2 podle času </text> </region> <region region-id="73" left="30" top="16977" width="511.5" height="142.5" align-x="73.5" align-y="17016" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="b2">dT</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="0">l</ml:id> <ml:real>1</ml:real> </ml:matrix> <ml:parens> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> </ml:matrix> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="2">l</ml:id> <ml:real>0</ml:real> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:matrix> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> </ml:matrix> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> </ml:matrix> </ml:apply> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="2">l</ml:id> <ml:real>0</ml:real> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:matrix> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="373"/> </region> <region region-id="74" left="30" top="17168.25" width="383.25" height="74.25" align-x="73.5" align-y="17208" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="b2">dT</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">l</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">l</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="374"/> </region> <region region-id="4238" left="30" top="17282.25" width="412.5" height="12" align-x="48.75" align-y="17292" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výpočet totálního diferenciálu (analogie derivace) transformační matice Tb3 podle času </text> </region> <region region-id="4240" left="30" top="17313" width="601.5" height="213" align-x="73.5" align-y="17352" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="b3">dT</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="0">l</ml:id> <ml:real>1</ml:real> </ml:matrix> <ml:parens> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="4"> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> </ml:matrix> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> </ml:matrix> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>-1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="2">l</ml:id> <ml:real>0</ml:real> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:matrix> </ml:apply> <ml:matrix rows="4" cols="4"> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:matrix> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> <ml:real>0</ml:real> 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subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">l</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="376"/> </region> <region region-id="1896" left="30" top="17702.25" width="453.75" height="228" align-x="30" align-y="17712" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> ROT1 MASS =<sp count="2"/>4.8824683e+01 KILOGRAM CENTER OF GRAVITY with respect to LCS1 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="4"/>-4.0325987e-02 -1.8024766e-06<sp count="2"/>7.3574162e-01<sp count="2"/>M INERTIA with respect to LCS1 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>4.6443693e+01 -7.9670815e-06<sp count="2"/>2.0478701e+00 Iyx Iyy Iyz -7.9670815e-06<sp count="2"/>4.7356949e+01<sp count="2"/>1.4573962e-04 Izx Izy Izz<sp count="2"/>2.0478701e+00<sp count="2"/>1.4573962e-04<sp count="2"/>1.4139746e+00 INERTIA at CENTER OF GRAVITY with respect to LCS1 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>2.0014124e+01 -4.4181788e-06<sp count="2"/>5.9926583e-01 Iyx Iyy Iyz -4.4181788e-06<sp count="2"/>2.0847982e+01<sp count="2"/>8.0990420e-05 Izx Izy Izz<sp count="2"/>5.9926583e-01<sp count="2"/>8.0990420e-05<sp count="2"/>1.3345766e+00 </text> </region> <region region-id="4265" left="30" top="17965.5" width="867.75" height="42" align-x="30" align-y="17982" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238" size="18"> <inlineAttr line-through="false">Pozor - pro Lagrangeovu pohybovou rovnici se použije matice setrvačnosti k lokálnímu souřadnému systému (ta první v pořadí), pro N-E vztahy byla předtím použita matice setrvačnosti k těžišti (druhá matice)</inlineAttr> </f> </text> </region> <region region-id="4249" left="30" top="18020.25" width="142.5" height="24" align-x="30" align-y="18030" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Článek 1</inlineAttr> </f> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">momenty k lokálnímu ss</inlineAttr> </f> </text> </region> <region region-id="4299" left="30" top="18056.25" width="107.25" height="21.75" align-x="51" align-y="18072" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">m</ml:id> <ml:apply> <ml:mult/> <ml:real>4.8824683</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="377"/> </region> <region region-id="4251" left="30" top="18086.25" width="107.25" height="21.75" align-x="51" align-y="18102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="x1">J</ml:id> <ml:apply> <ml:mult/> <ml:real>4.6443693</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="378"/> </region> <region region-id="4297" left="30" top="18110.25" width="124.5" height="21.75" align-x="54.75" align-y="18126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="xy1">J</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> <ml:real>7.9670815</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-6</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="379"/> </region> <region region-id="4296" left="192" top="18110.25" width="107.25" height="21.75" 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top="18134.25" width="118.5" height="21.75" align-x="216.75" align-y="18150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yz1">J</ml:id> <ml:apply> <ml:mult/> <ml:real>1.4573962</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-4</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="382"/> </region> <region region-id="4293" left="348" top="18140.25" width="81" height="15.75" align-x="369" align-y="18150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="z1">J</ml:id> <ml:real>1.4139746</ml:real> </ml:define> </math> <rendering item-idref="383"/> </region> <region region-id="4366" left="30" top="18188.25" width="354.75" height="12" align-x="51" align-y="18198" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Přepočet momentů setrvačnosti k osám na momenty setrvačnosti k rovinám </text> </region> <region region-id="4257" left="30" top="18214.5" width="102.75" height="31.5" align-x="54.75" align-y="18234" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="xx1">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="y1">J</ml:id> <ml:id xml:space="preserve" subscript="z1">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="x1">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="384"/> </region> <region region-id="4258" left="30" top="18250.5" width="102.75" height="31.5" align-x="54.75" align-y="18270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yy1">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="z1">J</ml:id> <ml:id xml:space="preserve" subscript="x1">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="y1">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="385"/> </region> <region region-id="4259" left="192" top="18230.25" width="68.25" height="74.25" align-x="219" align-y="18270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t11">P</ml:id> <ml:matrix rows="4" cols="1"> <ml:id xml:space="preserve" subscript="t11">x</ml:id> <ml:id xml:space="preserve" subscript="t11">y</ml:id> <ml:id xml:space="preserve" subscript="t11">z</ml:id> <ml:real>1</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="386"/> </region> <region region-id="4260" left="300" top="18230.25" width="124.5" height="73.5" align-x="326.25" align-y="18270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t11">P</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="1"> <ml:real>-0.040325987</ml:real> <ml:real>-1.8024766E-06</ml:real> <ml:real>0.7357416200000001</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="387"/> </region> <region region-id="4261" left="30" top="18286.5" width="102.75" height="31.5" align-x="54.75" align-y="18306" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="zz1">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="x1">J</ml:id> <ml:id xml:space="preserve" subscript="y1">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="z1">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="388"/> </region> <region region-id="4368" left="30" top="18326.25" width="135.75" height="12" align-x="50.25" align-y="18336" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Normální matice setrvačnosti </text> </region> <region region-id="93" left="30" top="18353.25" width="126.75" height="56.25" align-x="47.25" align-y="18384" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">J</ml:id> <ml:matrix rows="3" cols="3"> <ml:id xml:space="preserve" subscript="x1">J</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xy1">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xz1">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" 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<ml:real>46.443693</ml:real> <ml:real>7.9670815E-06</ml:real> <ml:real>-2.0478701</ml:real> <ml:real>7.9670815E-06</ml:real> <ml:real>47.356949</ml:real> <ml:real>-0.00014573962</ml:real> <ml:real>-2.0478701</ml:real> <ml:real>-0.00014573962</ml:real> <ml:real>1.4139746</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="390"/> </region> <region region-id="4370" left="30" top="18428.25" width="147.75" height="12" align-x="56.25" align-y="18438" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Homogenní matice setrvačnosti </text> </region> <region region-id="95" left="24" top="18456.75" width="228" height="76.5" align-x="43.5" align-y="18498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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<result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>1.1636153</ml:real> <ml:real>-7.9670815E-06</ml:real> <ml:real>2.0478701</ml:real> <ml:real>-1.9689035319371211</ml:real> <ml:real>-7.9670815E-06</ml:real> <ml:real>0.25035930000000306</ml:real> <ml:real>0.00014573962</ml:real> <ml:real>-8.80053486099178E-05</ml:real> <ml:real>2.0478701</ml:real> <ml:real>0.00014573962</ml:real> <ml:real>46.193333700000004</ml:real> <ml:real>35.922351366406467</ml:real> <ml:real>-1.9689035319371211</ml:real> <ml:real>-8.80053486099178E-05</ml:real> <ml:real>35.922351366406467</ml:real> <ml:real>48.824683</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="392"/> </region> <region region-id="97" left="24" top="18572.25" width="194.25" height="12" align-x="24" align-y="18582" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Kinetická energie prvního článku</inlineAttr> </f> </text> </region> <region region-id="98" left="24" top="18594.75" width="183.75" height="29.25" align-x="56.25" align-y="18612" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">tr</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="b1">dT</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="1">H</ml:id> </ml:apply> <ml:apply> <ml:transpose/> <ml:apply> <ml:id xml:space="preserve" subscript="b1">dT</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="393"/> </region> <region region-id="99" left="24" top="18638.25" width="669.75" height="12" align-x="24" align-y="18648" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Pro odvození výrazu pro kinetickou energii pro ruční použití v Lagr.rov. II. druhu provedeme symbolicky roznásobení (Shift+F9) </text> </region> <region region-id="100" left="24" top="18669" width="770.25" height="80.25" align-x="56.25" align-y="18714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">tr</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> 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<ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="xy1">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="yy1">J</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="xx1">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="xy1">J</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="xy1">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="yy1">J</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="395"/> </region> <region region-id="1060" left="24" top="18816.75" width="213" height="29.25" align-x="56.25" align-y="18834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="xx1">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="yy1">J</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="396"/> </region> <region region-id="103" left="24" top="18858.75" width="158.25" height="29.25" align-x="56.25" align-y="18876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="xx1">J</ml:id> <ml:id xml:space="preserve" subscript="yy1">J</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="397"/> </region> <region region-id="104" left="24" top="18894.75" width="117" height="29.25" align-x="56.25" align-y="18912" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="z1">J</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="398"/> </region> <region region-id="105" left="192" top="18902.25" width="79.5" height="12" align-x="192" align-y="18912" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> jen rotace </text> </region> <region region-id="1898" left="24" top="18962.25" width="474" height="228" align-x="24" align-y="18972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> TRAN2 MASS =<sp count="2"/>4.2894906e+01 KILOGRAM CENTER OF GRAVITY with respect to LCS2 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="4"/>-7.2368752e-02<sp count="2"/>0.0000000e+00 -4.7439674e-02<sp count="2"/>M INERTIA with respect to LCS2 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>1.0344896e+00<sp count="2"/>0.0000000e+00 -1.2186605e-01 Iyx Iyy Iyz<sp count="2"/>0.0000000e+00<sp count="2"/>1.7935719e+00<sp count="2"/>0.0000000e+00 Izx Izy Izz -1.2186605e-01<sp count="2"/>0.0000000e+00<sp count="2"/>1.4614205e+00 INERTIA at CENTER OF GRAVITY with respect to LCS2 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>9.3795366e-01<sp count="2"/>0.0000000e+00<sp count="2"/>2.5398594e-02 Iyx Iyy Iyz<sp count="2"/>0.0000000e+00<sp count="2"/>1.4723852e+00<sp count="2"/>0.0000000e+00 Izx Izy Izz<sp count="2"/>2.5398594e-02<sp count="2"/>0.0000000e+00<sp count="2"/>1.2367697e+00 </text> </region> <region region-id="4303" left="24" top="19226.25" width="129" height="24" align-x="24" align-y="19236" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Článek 2</inlineAttr> </f> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">momenty k lokálnímu ss</inlineAttr> </f> </text> </region> <region region-id="4331" left="24" top="19274.25" width="107.25" height="21.75" align-x="45" align-y="19290" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">m</ml:id> <ml:apply> <ml:mult/> <ml:real>4.2894906</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="399"/> </region> <region region-id="4332" left="24" top="19304.25" width="81" height="15.75" align-x="45" align-y="19314" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="x2">J</ml:id> <ml:real>1.0344896</ml:real> </ml:define> </math> <rendering item-idref="400"/> </region> <region region-id="4353" left="24" top="19328.25" width="39.75" height="15.75" align-x="48.75" align-y="19338" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="xy2">J</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="401"/> </region> <region region-id="4354" left="174" top="19328.25" width="81" height="15.75" align-x="195" align-y="19338" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="y2">J</ml:id> <ml:real>1.7935719</ml:real> </ml:define> </math> <rendering item-idref="402"/> </region> <region region-id="4350" left="24" top="19346.25" width="124.5" height="21.75" align-x="48.75" align-y="19362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="xz2">J</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:mult/> <ml:real>1.2186605</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="403"/> </region> <region region-id="4352" left="174" top="19352.25" width="39.75" height="15.75" align-x="198.75" align-y="19362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yz2">J</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="404"/> </region> <region region-id="4351" left="288" top="19352.25" width="81" height="15.75" align-x="309" align-y="19362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="z2">J</ml:id> <ml:real>1.4614205</ml:real> </ml:define> </math> <rendering item-idref="405"/> </region> <region region-id="4375" left="24" top="19394.25" width="354.75" height="12" align-x="45" align-y="19404" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Přepočet momentů setrvačnosti k osám na momenty setrvačnosti k rovinám </text> </region> <region region-id="115" left="30" top="19420.5" width="102.75" height="31.5" align-x="54.75" align-y="19440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="xx2">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="y2">J</ml:id> <ml:id xml:space="preserve" subscript="z2">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="x2">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="406"/> </region> <region region-id="4361" left="192" top="19430.25" width="68.25" height="74.25" align-x="219" align-y="19470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t22">P</ml:id> <ml:matrix rows="4" cols="1"> <ml:id xml:space="preserve" subscript="t22">x</ml:id> <ml:id xml:space="preserve" subscript="t22">y</ml:id> <ml:id xml:space="preserve" subscript="t22">z</ml:id> <ml:real>1</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="407"/> </region> <region region-id="4362" left="300" top="19433.25" width="88.5" height="67.5" align-x="326.25" align-y="19470" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t22">P</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="1"> <ml:real>-0.072368752000000008</ml:real> <ml:real>0</ml:real> <ml:real>-0.047439674</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="408"/> </region> <region region-id="119" left="30" top="19456.5" width="102.75" height="31.5" align-x="54.75" align-y="19476" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yy2">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="z2">J</ml:id> <ml:id xml:space="preserve" subscript="x2">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="y2">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="409"/> </region> <region region-id="121" left="30" top="19492.5" width="102.75" height="31.5" align-x="54.75" align-y="19512" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="zz2">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="x2">J</ml:id> <ml:id xml:space="preserve" subscript="y2">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="z2">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="410"/> </region> <region region-id="4376" left="30" top="19538.25" width="135.75" height="12" align-x="50.25" align-y="19548" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Normální matice setrvačnosti </text> </region> <region region-id="4384" left="30" top="19571.25" width="126.75" height="56.25" align-x="47.25" align-y="19602" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">J</ml:id> <ml:matrix rows="3" cols="3"> <ml:id xml:space="preserve" subscript="x2">J</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xy2">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xz2">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xy2">J</ml:id> </ml:apply> <ml:id xml:space="preserve" 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<ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="xx2">J</ml:id> <ml:id xml:space="preserve" subscript="zz2">J</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">l</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="2">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t22">x</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="2">l</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="2">m</ml:id> </ml:apply> 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<ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="y2">J</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">l</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="2">m</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t22">x</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="2">l</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="2">m</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="2">m</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="424"/> </region> <region region-id="1905" left="312" top="20402.25" width="57.75" height="192" align-x="324" align-y="20412" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve" subscript="2">K</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>0</ml:real> <ml:real>0.22214456666777627</ml:real> <ml:real>0.88820446956187715</ml:real> <ml:real>1.9970819737411851</ml:real> <ml:real>3.5470247590837416</ml:real> <ml:real>5.5357361571256609</ml:real> <ml:real>7.9605184133456506</ml:real> <ml:real>10.818438422976984</ml:real> <ml:real>14.106503354114697</ml:real> <ml:real>17.821832551456382</ml:real> <ml:real>21.961812412232625</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="425"/> </resultFormat> </math> <rendering item-idref="426"/> </region> <region region-id="4397" left="30" top="20414.25" width="236.25" height="24" align-x="48" align-y="20424" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Důležitá je neustálá kontrola úprav výrazu jeho vyčíslením před úpravou a po úpravě </text> </region> <region region-id="1907" left="24" top="20648.25" width="551.25" height="228" align-x="24" align-y="20658" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> TRAN3 MASS =<sp count="2"/>5.9261161e+01 KILOGRAM CENTER OF GRAVITY with respect to LCS3 coordinate frame: X<sp count="3"/>Y<sp count="3"/>Z<sp count="5"/>2.5740416e-03<sp count="2"/>0.0000000e+00 -3.7039760e-01<sp count="2"/>M INERTIA with respect to LCS3 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>3.3435680e+01<sp count="2"/>0.0000000e+00<sp count="2"/>1.9296398e-01 Iyx Iyy Iyz<sp count="2"/>0.0000000e+00<sp count="2"/>3.4142950e+01<sp count="2"/>0.0000000e+00 Izx Izy Izz<sp count="2"/>1.9296398e-01<sp count="2"/>0.0000000e+00<sp count="2"/>1.0075258e+00 INERTIA at CENTER OF GRAVITY with respect to LCS3 coordinate frame:<sp count="2"/>(KILOGRAM * M^2) INERTIA TENSOR: Ixx Ixy Ixz<sp count="2"/>2.5305381e+01<sp count="2"/>0.0000000e+00<sp count="2"/>1.3646327e-01 Iyx Iyy Iyz<sp count="2"/>0.0000000e+00<sp count="2"/>2.6012259e+01<sp count="2"/>0.0000000e+00 Izx Izy Izz<sp count="2"/>1.3646327e-01<sp count="2"/>0.0000000e+00<sp count="2"/>1.0071331e+00 </text> </region> <region region-id="4415" left="24" top="20894.25" width="129" height="24" align-x="24" align-y="20904" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Článek 3</inlineAttr> </f> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">momenty k lokálnímu ss</inlineAttr> </f> </text> </region> <region region-id="4420" left="24" top="20930.25" width="107.25" height="21.75" align-x="45" align-y="20946" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:apply> <ml:mult/> <ml:real>5.9261161</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="427"/> </region> <region region-id="4419" left="24" top="20960.25" width="107.25" height="21.75" align-x="45" align-y="20976" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="x3">J</ml:id> <ml:apply> <ml:mult/> <ml:real>3.3435680</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="428"/> </region> <region region-id="4439" left="24" top="20990.25" width="84.75" height="15.75" align-x="48.75" align-y="21000" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="xy3">J</ml:id> <ml:real>0.0000000</ml:real> </ml:define> </math> <rendering item-idref="429"/> </region> <region region-id="4440" left="174" top="20984.25" width="107.25" height="21.75" align-x="195" align-y="21000" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="y3">J</ml:id> <ml:apply> <ml:mult/> <ml:real>3.4142950</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="430"/> </region> <region region-id="4436" left="24" top="21008.25" width="118.5" height="21.75" align-x="48.75" align-y="21024" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="xz3">J</ml:id> <ml:apply> <ml:mult/> <ml:real>1.9296398</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="431"/> </region> <region region-id="4438" left="174" top="21014.25" width="84.75" height="15.75" align-x="198.75" align-y="21024" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yz3">J</ml:id> <ml:real>0.0000000</ml:real> </ml:define> </math> <rendering item-idref="432"/> </region> <region region-id="4437" left="312" top="21014.25" width="81" height="15.75" align-x="333" align-y="21024" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="z3">J</ml:id> <ml:real>1.0075258</ml:real> </ml:define> </math> <rendering item-idref="433"/> </region> <region region-id="4445" left="24" top="21056.25" width="354.75" height="12" align-x="45" align-y="21066" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Přepočet momentů setrvačnosti k osám na momenty setrvačnosti k rovinám </text> </region> <region region-id="4410" left="24" top="21082.5" width="102.75" height="31.5" align-x="48.75" align-y="21102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="xx3">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="y3">J</ml:id> <ml:id xml:space="preserve" subscript="z3">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="x3">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="434"/> </region> <region region-id="4411" left="24" top="21118.5" width="102.75" height="31.5" align-x="48.75" align-y="21138" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yy3">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="z3">J</ml:id> <ml:id xml:space="preserve" subscript="x3">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="y3">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="435"/> </region> <region region-id="1908" left="192" top="21098.25" width="68.25" height="74.25" align-x="219" align-y="21138" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t33">P</ml:id> <ml:matrix rows="4" cols="1"> <ml:id xml:space="preserve" subscript="t33">x</ml:id> <ml:id xml:space="preserve" subscript="t33">y</ml:id> <ml:id xml:space="preserve" subscript="t33">z</ml:id> <ml:real>1</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="436"/> </region> <region region-id="1910" left="294" top="21098.25" width="118.5" height="73.5" align-x="320.25" align-y="21138" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t33">P</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="1"> <ml:real>0.0025740416</ml:real> <ml:real>0</ml:real> <ml:real>-0.3703976</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="437"/> </region> <region region-id="4412" left="24" top="21154.5" width="102.75" height="31.5" align-x="48.75" align-y="21174" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="zz3">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="x3">J</ml:id> <ml:id xml:space="preserve" subscript="y3">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="z3">J</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="438"/> </region> <region region-id="4446" left="24" top="21212.25" width="135.75" height="12" align-x="44.25" align-y="21222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Normální matice setrvačnosti </text> </region> <region region-id="4449" left="24" top="21239.25" width="126.75" height="56.25" align-x="41.25" align-y="21270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">J</ml:id> <ml:matrix rows="3" cols="3"> <ml:id xml:space="preserve" subscript="x3">J</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xy3">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xz3">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xy3">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="y3">J</ml:id> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="yz3">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="xz3">J</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="yz3">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="z3">J</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="439"/> </region> <region region-id="4448" left="246" top="21242.25" width="161.25" height="49.5" align-x="262.5" align-y="21270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">J</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="3" cols="3"> <ml:real>33.43568</ml:real> <ml:real>0</ml:real> <ml:real>-0.19296398</ml:real> <ml:real>0</ml:real> <ml:real>34.14295</ml:real> <ml:real>0</ml:real> <ml:real>-0.19296398</ml:real> <ml:real>0</ml:real> <ml:real>1.0075258</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="440"/> </region> <region region-id="4447" left="24" top="21320.25" width="147.75" height="12" align-x="50.25" align-y="21330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Homogenní matice setrvačnosti </text> </region> <region region-id="158" left="24" top="21342.75" width="228" height="76.5" align-x="43.5" align-y="21384" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">H</ml:id> <ml:matrix rows="4" cols="4"> <ml:id xml:space="preserve" subscript="xx3">J</ml:id> <ml:id xml:space="preserve" subscript="xy3">J</ml:id> <ml:id xml:space="preserve" subscript="xz3">J</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="t33">x</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="xy3">J</ml:id> <ml:id xml:space="preserve" subscript="yy3">J</ml:id> <ml:id xml:space="preserve" subscript="yz3">J</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="t33">y</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="xz3">J</ml:id> <ml:id xml:space="preserve" subscript="yz3">J</ml:id> <ml:id xml:space="preserve" subscript="zz3">J</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="t33">z</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="t33">x</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="t33">y</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="t33">z</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="3">m</ml:id> </ml:matrix> </ml:define> </math> <rendering item-idref="441"/> </region> <region region-id="159" left="270" top="21347.25" width="186.75" height="67.5" align-x="288.75" align-y="21384" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="3">H</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="4"> <ml:real>0.85739790000000227</ml:real> <ml:real>0</ml:real> <ml:real>0.19296398</ml:real> <ml:real>0.15254069367829762</ml:real> <ml:real>0</ml:real> <ml:real>0.15012790000000109</ml:real> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:real>0.19296398</ml:real> <ml:real>0</ml:real> <ml:real>33.285552100000004</ml:real> <ml:real>-21.9501918076136</ml:real> <ml:real>0.15254069367829762</ml:real> <ml:real>0</ml:real> <ml:real>-21.9501918076136</ml:real> <ml:real>59.261161</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="442"/> </region> <region region-id="160" left="24" top="21458.25" width="195.75" height="12" align-x="24" align-y="21468" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Kinetická energie třetího článku</inlineAttr> </f> </text> </region> <region region-id="161" left="24" top="21480.75" width="183.75" height="29.25" align-x="56.25" align-y="21498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> 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xml:space="preserve">t</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>0</ml:real> <ml:real>0.83740675238908024</ml:real> <ml:real>3.3493738846883394</ml:real> <ml:real>7.5352853737020222</ml:real> <ml:real>13.394572861856371</ml:real> <ml:real>20.927336933791629</ml:real> <ml:real>30.135091556700644</ml:real> <ml:real>41.021523044489456</ml:real> <ml:real>53.593147357480753</ml:real> <ml:real>67.859757921022023</ml:real> <ml:real>83.834580654695827</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="444"/> </resultFormat> </math> <rendering item-idref="445"/> </region> <region region-id="4465" left="24" top="21704.25" width="669.75" height="12" align-x="24" align-y="21714" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Pro odvození výrazu pro kinetickou energii pro ruční použití v Lagr.rov. II. druhu provedeme symbolicky roznásobení (Shift+F9) </text> </region> <region region-id="164" left="24" top="21740.25" width="1416.75" height="81" align-x="56.25" align-y="21786" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">tr</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:matrix rows="4" cols="4"> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> 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is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Po symbolickém vynásobení </text> </region> <region region-id="1016" left="24" top="21858.75" width="5332.5" height="29.25" align-x="56.25" align-y="21876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>-1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> 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<ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="2">l</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="3">m</ml:id> <ml:id xml:space="preserve" subscript="t33">x</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="501"/> </region> <region region-id="4942" left="36" top="24110.25" width="319.5" height="12" align-x="57" align-y="24120" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výsledný upravený výraz pro kinetickou energii celého mechanismu </text> </region> <region region-id="4940" left="36" top="24138.75" width="510.75" height="29.25" align-x="63.75" align-y="24156" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> 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<ml:real>2112.4269657666896</ml:real> <ml:real>2129.4577152722641</ml:real> <ml:real>2148.4920823667294</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="510"/> </resultFormat> </math> <rendering item-idref="511"/> </region> <region region-id="5027" left="36" top="24386.25" width="405" height="12" align-x="36" align-y="24396" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> M<f family="Arial CE" charset="238"> <inlineAttr line-through="false">ísto hmotnostních parametrů pro zjednodušení použity nové konstanty</inlineAttr> </f> </text> </region> <region region-id="5038" left="36" top="24416.25" width="264" height="15.75" align-x="54.75" align-y="24426" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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</ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="512"/> </region> <region region-id="5039" left="36" top="24434.25" width="90" height="15.75" align-x="54.75" align-y="24444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">g</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="2">m</ml:id> <ml:id xml:space="preserve" subscript="3">m</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="513"/> </region> <region region-id="5079" left="36" top="24458.25" width="302.25" height="12" align-x="57" align-y="24468" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výsledný upravený výraz pro potenciální energii celého systému </text> </region> <region region-id="5044" left="36" top="24488.25" width="104.25" height="15.75" align-x="63" align-y="24498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">P</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">e</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="514"/> </region> <region region-id="5045" left="162" top="24488.25" width="70.5" height="192" align-x="171" align-y="24498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">P</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="11" cols="1"> <ml:real>2048.3112029221747</ml:real> <ml:real>2049.31301171662</ml:real> <ml:real>2052.3184380999569</ml:real> <ml:real>2057.3274820721845</ml:real> <ml:real>2064.3401436333033</ml:real> <ml:real>2073.3564227833135</ml:real> <ml:real>2084.3763195222145</ml:real> <ml:real>2097.3998338500064</ml:real> <ml:real>2112.42696576669</ml:real> <ml:real>2129.4577152722641</ml:real> <ml:real>2148.49208236673</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat> <table item-idref="515"/> </resultFormat> </math> <rendering item-idref="516"/> </region> <region region-id="202" left="30" top="24703.5" width="578.25" height="21" align-x="30" align-y="24720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238" size="18"> <inlineAttr line-through="false">Výpočet zobecněné síly pomocí Lagrangeovy pohybové rovnice II. druhu</inlineAttr> </f> </text> </region> <region region-id="5160" left="36" top="24744" width="144" height="46.5" align-x="36" align-y="24744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="517" display-width="142.5" display-height="45"/> </picture> <rendering item-idref="518"/> </region> <region region-id="5196" left="36" top="24812.25" width="99.75" height="12" align-x="36" align-y="24822" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Výpočet τ1</inlineAttr> </f> </text> </region> <region region-id="5195" left="36" top="24836.25" width="255" height="12" align-x="54.75" align-y="24846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výpočet prvního členu Lagr. pohybové rovnice - L11(t) </text> </region> <region region-id="5194" left="36" top="24860.25" width="345" height="12" align-x="36" align-y="24870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Parciální derivaci K(t) podle dq1(t) je třeba udělat ručně:</inlineAttr> </f> </text> </region> <region region-id="5193" left="36" top="24888.75" width="510.75" height="29.25" align-x="63.75" align-y="24906" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> 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<ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="519"/> </region> <region region-id="5192" left="36" top="24920.25" width="282.75" height="21.75" align-x="69.75" align-y="24936" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> 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<ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="520"/> </region> <region region-id="5191" left="36" top="24956.25" width="372" height="12" align-x="36" align-y="24966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Derivaci podle času provede Mathcad, je ji potřeba ale ručně upravit</inlineAttr> </f> <sp/> </text> </region> <region region-id="5190" left="36" top="24996" width="305.25" height="31.5" align-x="74.25" align-y="25014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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xml:space="preserve" subscript="0">a</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> </ml:apply> </ml:define> </math> <rendering item-idref="521"/> </region> <region region-id="5189" left="36" top="25038" width="540.75" height="31.5" align-x="74.25" align-y="25056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L11</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="522"/> </region> <region region-id="5188" left="36" top="25082.25" width="519.75" height="21.75" align-x="74.25" align-y="25098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L11</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="523"/> </region> <region region-id="5187" left="36" top="25142.25" width="218.25" height="12" align-x="36" align-y="25152" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Druhý člen Lagr. rovnice L12(t)</inlineAttr> </f> </text> </region> <region region-id="5186" left="36" top="25166.25" width="569.25" height="12" align-x="36" align-y="25176" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Mathcad neumí symbolicky, proto ručně, v kinetické energii nikde není q1(t), proto výsledek druhého členu je 0</inlineAttr> </f> </text> </region> <region region-id="5185" left="36" top="25196.25" width="53.25" height="13.5" align-x="74.25" align-y="25206" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L12</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="524"/> </region> <region region-id="5184" left="36" top="25232.25" width="200.25" height="12" align-x="36" align-y="25242" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Třetí člen L13(t)</inlineAttr> </f> </text> </region> <region region-id="5183" left="36" top="25262.25" width="104.25" height="15.75" align-x="63" align-y="25272" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">P</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">e</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="525"/> </region> <region region-id="5182" left="36" top="25290" width="108" height="33.75" align-x="36" align-y="25308" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="1">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:boundVars> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">e</ml:id> </ml:apply> </ml:parens> </ml:lambda> </ml:apply> </math> <rendering item-idref="526"/> </region> <region region-id="5181" left="36" top="25334.25" width="109.5" height="12" align-x="36" align-y="25344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> roven také nule </text> </region> <region region-id="5198" left="36" top="25370.25" width="264" height="12" align-x="57" align-y="25380" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výsledná zobecněná síla τ1 je tedy rovna prvnímu členu </text> </region> <region region-id="5180" left="36" top="25412.25" width="513" height="21.75" align-x="67.5" align-y="25428" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="527"/> </region> <region region-id="5200" left="36" top="25472.25" width="426.75" height="12" align-x="60" align-y="25482" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Porovnání s výsledkem získaným z Newton-Eulerových vztahů (bez vlivu vnitřních převodů) </text> </region> <region region-id="777" left="36" top="25500" width="394.5" height="307.5" align-x="36" align-y="25500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="528"/> <rendering item-idref="529"/> </region> <region region-id="1920" left="504" top="25500" width="421.5" height="295.5" align-x="504" align-y="25500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="530"/> <rendering item-idref="531"/> </region> <region region-id="5335" left="30" top="25874.25" width="240.75" height="12" align-x="30" align-y="25884" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Druhá zobecněná síla τ2, první člen L21(t) </text> </region> <region region-id="5324" left="30" top="25904.25" width="246" height="12" align-x="30" align-y="25914" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Kinetická energie po ruční derivaci podle dq2 </text> </region> <region region-id="5325" left="30" top="25926.75" width="510.75" height="29.25" align-x="57.75" align-y="25944" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="532"/> </region> <region region-id="5326" left="30" top="25976.25" width="51" height="15.75" align-x="63.75" align-y="25986" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> </ml:apply> </math> <rendering item-idref="533"/> </region> <region region-id="5327" left="30" top="25998" width="115.5" height="31.5" align-x="68.25" align-y="26016" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L21</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> </ml:apply> </ml:parens> </ml:lambda> </ml:apply> </ml:define> </math> <rendering item-idref="534"/> </region> <region region-id="5328" left="30" top="26042.25" width="103.5" height="15.75" align-x="68.25" align-y="26052" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L21</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="535"/> </region> <region region-id="5329" left="30" top="26084.25" width="386.25" height="12" align-x="30" align-y="26094" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">druhý člen L22(t) roven nule - v kinetické energii není nikde q2(t)</inlineAttr> </f> </text> </region> <region region-id="5330" left="30" top="26112" width="108" height="33.75" align-x="30" align-y="26130" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:boundVars> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">e</ml:id> </ml:apply> </ml:parens> </ml:lambda> </ml:apply> </math> <rendering item-idref="536"/> </region> <region region-id="5205" left="30" top="26162.25" width="280.5" height="12" align-x="30" align-y="26172" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">třetí člen L23(t) - derivace potenciální energie podle q2(t)</inlineAttr> </f> </text> </region> <region region-id="5339" left="30" top="26186.25" width="104.25" height="15.75" align-x="57" align-y="26196" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">P</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">e</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="537"/> </region> <region region-id="5331" left="30" top="26210.25" width="58.5" height="15.75" align-x="68.25" align-y="26220" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L23</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:id xml:space="preserve" subscript="1">e</ml:id> </ml:define> </math> <rendering item-idref="538"/> </region> <region region-id="5332" left="30" top="26240.25" width="158.25" height="12" align-x="30" align-y="26250" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Druhá zobecnìná síla </text> </region> <region region-id="5333" left="30" top="26264.25" width="120.75" height="15.75" align-x="61.5" align-y="26274" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="2">τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="1">e</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="539"/> </region> <region region-id="5347" left="30" top="26336.25" width="426.75" height="12" align-x="54" align-y="26346" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Porovnání s výsledkem získaným z Newton-Eulerových vztahů (bez vlivu vnitřních převodů) </text> </region> <region region-id="1921" left="6" top="26364" width="438" height="286.5" align-x="6" align-y="26364" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="540"/> <rendering item-idref="541"/> </region> <region region-id="1923" left="492" top="26370" width="429" height="280.5" align-x="492" align-y="26370" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="542"/> <rendering item-idref="543"/> </region> <region region-id="5379" left="30" top="26726.25" width="455.25" height="12" align-x="30" align-y="26736" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Třetí zob síla, první člen L31(t), derivace K(t) ručně derivaci podle dq3(t) a pak podle času</inlineAttr> </f> </text> </region> <region region-id="5378" left="30" top="26766.75" width="510.75" height="29.25" align-x="57.75" align-y="26784" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">K</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="2">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="544"/> </region> <region region-id="5377" left="30" top="26804.25" width="132" height="12" align-x="50.25" align-y="26814" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Derivace ručně podle dq3(t) </text> </region> <region region-id="5376" left="30" top="26828.25" width="113.25" height="15.75" align-x="85.5" align-y="26838" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="545"/> </region> <region region-id="5375" left="30" top="26852.25" width="96" height="12" align-x="50.25" align-y="26862" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Derivace podle času </text> </region> <region region-id="5374" left="30" top="26868" width="131.25" height="31.5" align-x="30" align-y="26886" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> </ml:apply> </math> <rendering item-idref="546"/> </region> <region region-id="5373" left="30" top="26910" width="134.25" height="31.5" align-x="96" align-y="26928" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="547"/> </region> <region region-id="5372" left="30" top="26960.25" width="171.75" height="15.75" align-x="68.25" align-y="26970" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L31</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="548"/> </region> <region region-id="5371" left="30" top="27032.25" width="240.75" height="12" align-x="30" align-y="27042" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">druhý člen L32(t) , parciálně K(t) podle q3(t)</inlineAttr> </f> </text> </region> <region region-id="5370" left="30" top="27060.75" width="175.5" height="29.25" align-x="109.5" align-y="27078" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="1">a</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="549"/> </region> <region region-id="5369" left="30" top="27096.75" width="200.25" height="29.25" align-x="68.25" align-y="27114" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">L32</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="550"/> </region> <region region-id="5368" left="30" top="27134.25" width="345" height="12" align-x="30" align-y="27144" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">třetí člen L33(t) derivace P(t) podle q3(t) - nikde není, roven nule</inlineAttr> </f> </text> </region> <region region-id="5367" left="30" top="27162" width="108" height="33.75" align-x="30" align-y="27180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:boundVars> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="2">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">e</ml:id> </ml:apply> </ml:parens> </ml:lambda> </ml:apply> </math> <rendering item-idref="551"/> </region> <region region-id="5366" left="30" top="27240.75" width="330.75" height="29.25" align-x="61.5" align-y="27258" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="552"/> </region> <region region-id="5365" left="408" top="27248.25" width="340.5" height="12" align-x="408" align-y="27258" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> První člen je zrychlující síla, druhý tečná, třetí odstředivá síla </text> </region> <region region-id="5382" left="30" top="27314.25" width="426.75" height="12" align-x="54" align-y="27324" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Porovnání s výsledkem získaným z Newton-Eulerových vztahů (bez vlivu vnitřních převodů) </text> </region> <region region-id="801" left="6" top="27342" width="364.5" height="331.5" align-x="6" align-y="27342" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="553"/> <rendering item-idref="554"/> </region> <region region-id="1925" left="468" top="27348" width="391.5" height="331.5" align-x="468" align-y="27348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="555"/> <rendering item-idref="556"/> </region> <region region-id="5509" left="36" top="27722.25" width="304.5" height="12" align-x="57" align-y="27732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Výsledné Lagrangeovy pohybové rovnice - bez vnitřních převodů </text> </region> <region region-id="5495" left="36" top="27758.25" width="474" height="21.75" align-x="67.5" align-y="27774" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> 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xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="2">τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="2">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="1">e</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="558"/> </region> <region region-id="5497" left="36" top="27828.75" width="330.75" height="29.25" align-x="67.5" align-y="27846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="559"/> </region> <region region-id="5498" left="36" top="27883.5" width="601.5" height="42" align-x="36" align-y="27900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238" size="18"> <inlineAttr line-through="false">Zahrnutí vlivu vnitřních převodů a rozvodů na dynamiku mechanismu (redukované momenty a hmotnosti)</inlineAttr> </f> </text> </region> <region region-id="5524" left="36" top="27962.25" width="100.5" height="15.75" align-x="58.5" align-y="27972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="p1">J</ml:id> <ml:real>5.8702800000</ml:real> </ml:define> </math> <rendering item-idref="560"/> </region> <region region-id="5525" left="210" top="27962.25" width="577.5" height="12" align-x="210" align-y="27972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Zahrnutí vlivu momentu setrvačnosti rotoru motoru, převodovky a vnitřních kroužků velkých ložisek</inlineAttr> </f> </text> </region> <region region-id="5526" left="36" top="27986.25" width="87.75" height="15.75" align-x="63.75" align-y="27996" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math 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<ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="p12">m</ml:id> <ml:id xml:space="preserve" subscript="p21">J</ml:id> </ml:define> </math> <rendering item-idref="562"/> </region> <region region-id="5515" left="210" top="28010.25" width="420" height="12" align-x="210" align-y="28020" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Zahrnutí vlivu zrychlení ROT1 na vnitřní převody TRAN2</inlineAttr> </f> </text> </region> <region region-id="5516" left="36" top="28034.25" width="104.25" height="15.75" align-x="62.25" align-y="28044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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<ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="p3">m</ml:id> <ml:real>51.5751826083</ml:real> </ml:define> </math> <rendering item-idref="564"/> </region> <region region-id="5523" left="210" top="28058.25" width="747.75" height="12" align-x="210" align-y="28068" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">Zahrnutí zvýšení redukované hmotnosti vlivem zrychlení rotoru motoru MOT3, ozubeného kola a matice pohybového šroubu (řemen neuvažován)</inlineAttr> </f> </text> </region> <region region-id="5532" left="36" top="28088.25" width="249.75" height="12" align-x="36" align-y="28098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Pozn. - Nejsou uvažovány gyroskopické efekty </text> </region> <region region-id="5549" left="36" top="28154.25" width="579.75" height="21.75" align-x="67.5" align-y="28170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> 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background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Zavedení nových koeficientů - zahrnují hmotnostní parametry a polohy těžišť </text> </region> <region region-id="5584" left="36" top="28298.25" width="66.75" height="15.75" align-x="54.75" align-y="28308" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="0">a</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="0">a</ml:id> <ml:id xml:space="preserve" subscript="p1">J</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="568"/> </region> <region region-id="5585" left="36" top="28322.25" width="70.5" height="15.75" align-x="54.75" align-y="28332" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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subscript="1">e</ml:id> <ml:real>0</ml:real> </ml:matrix> </ml:apply> </ml:parens> </ml:define> </math> <rendering item-idref="597"/> </region> <region region-id="5669" left="42" top="29509.5" width="548.25" height="75.75" align-x="70.5" align-y="29550" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">Τ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id 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xml:space="preserve" subscript="2">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="1">e</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="1">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="0">c</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">ddq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="1">dq</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="2">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="1">a</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:matrix> </ml:define> </math> <rendering item-idref="598"/> </region> <region region-id="5673" left="42" top="29606.25" width="516.75" height="12" align-x="60" align-y="29616" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> Opačná úloha - zjištění počátečního vektoru zrychlení DDQ(t)<sp count="2"/>při buzení známým průběhem zobecněných sil </text> </region> <region region-id="5671" left="42" top="29654.25" width="771.75" height="70.5" align-x="85.5" align-y="29694" show-border="false" 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</ml:apply> </ml:matrix> <ml:matrix rows="3" cols="1"> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="1">e</ml:id> <ml:real>0</ml:real> </ml:matrix> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:matrix rows="3" cols="3"> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="2">a</ml:id> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="1">a</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="3">q</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="0">a</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="0">f</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="0">f</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="0">b</ml:id> <ml:real>0</ml:real> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="0">d</ml:id> </ml:apply> <ml:real>0</ml:real> <ml:id xml:space="preserve" subscript="0">c</ml:id> </ml:matrix> <ml:real>-1</ml:real> </ml:apply> <ml:matrix rows="3" cols="1"> <ml:apply> <ml:id xml:space="preserve" subscript="1">τ</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="2">τ</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve" subscript="3">τ</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:matrix> </ml:apply> </ml:apply> </ml:parens> </ml:define> </math> <rendering item-idref="599"/> </region> <region region-id="1327" left="90" top="29808" width="190.5" height="157.5" align-x="90" align-y="29808" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="600"/> <rendering item-idref="601"/> </region> <region region-id="1328" left="462" top="29808" width="175.5" height="157.5" align-x="462" align-y="29808" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="602"/> <rendering item-idref="603"/> </region> <region region-id="1366" left="330" top="29858.25" width="143.25" height="24" align-x="341.25" align-y="29868" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial CE" charset="238"> <inlineAttr line-through="false">stejné jako požadované zrychlení</inlineAttr> </f> </text> </region> </regions> <binaryContent> <item item-id="1" 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