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Display information for equation id:math.1346.19 on revision:1346

* Page found: Mechanik des starren Körpers (eq math.1346.19)

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Hash: c55e0e028c63e1af0c2ddc81959f68b9

TeX (original user input):

\begin{align}
  & T=\frac{1}{2}\int_{{}}^{{}}{{{d}^{3}}x\rho (\bar{x}){{\left( \bar{V}+\bar{\omega }\times \bar{x} \right)}^{2}}}=\frac{1}{2}\int_{{}}^{{}}{{{d}^{3}}x\rho (\bar{x}){{V}^{2}}+\frac{1}{2}\sum\limits_{m=1}^{3}{\sum\limits_{n=1}^{3}{{}}{{\omega }^{m}}{{J}_{mn}}}{{\omega }^{n}}} \\ 
 &  \\ 
\end{align}

TeX (checked):

{\begin{aligned}&T={\frac {1}{2}}\int _{}^{}{{{d}^{3}}x\rho ({\bar {x}}){{\left({\bar {V}}+{\bar {\omega }}\times {\bar {x}}\right)}^{2}}}={\frac {1}{2}}\int _{}^{}{{{d}^{3}}x\rho ({\bar {x}}){{V}^{2}}+{\frac {1}{2}}\sum \limits _{m=1}^{3}{\sum \limits _{n=1}^{3}{}{{\omega }^{m}}{{J}_{mn}}}{{\omega }^{n}}}\\&\\\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

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MathML (experimentell; keine Bilder) rendering

MathML (3.207 KB / 538 B) :

T=12d3xρ(x¯)(V¯+ω¯×x¯)2=12d3xρ(x¯)V2+12m=13n=13ωmJmnωn
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>T</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>x</mi><mi>&#x03C1;</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">)</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>V</mi><mo>¯</mo></mover></mrow></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>&#x03C9;</mi><mo>¯</mo></mover></mrow></mrow><mo>&#x00D7;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>x</mi><mi>&#x03C1;</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">)</mo><msup><mi>V</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></munderover><mrow data-mjx-texclass="ORD"><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></munderover><msup><mi>&#x03C9;</mi><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msup><msub><mi>J</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><mi>n</mi></mrow></mrow></msub></mrow><msup><mi>&#x03C9;</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup></mrow></mtd></mtr><mtr><mtd></mtd><mtd></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Mechanik des starren Körpers page

Identifiers

  • T
  • x
  • ρ
  • x¯
  • V¯
  • ω¯
  • x¯
  • x
  • ρ
  • x¯
  • V
  • m
  • n
  • ω
  • m
  • Jmn
  • ω
  • n

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