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Display information for equation id:math.2006.12 on revision:2006

* Page found: Kinetische Energie und Trägheitstensor (eq math.2006.12)

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Kinetische Energie und Trägheitstensor Eq: math.2016.12

Hash: 2040327d0a223561aff6e3ee07f6c855

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}}+\left( \bar{V}\times \bar{\omega } \right)\int_{{}}^{{}}{{{d}^{3}}x\rho (\bar{x})\bar{x}+\frac{1}{2}\sum\limits_{m=1}^{3}{\sum\limits_{n=1}^{3}{{}}{{\omega }^{m}}{{J}_{mn}}}{{\omega }^{n}}}} \\
 & mit\int_{{}}^{{}}{{{d}^{3}}x\rho (\bar{x})\bar{x}=0} \\
\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}}+\left({\bar {V}}\times {\bar {\omega }}\right)\int _{}^{}{{{d}^{3}}x\rho ({\bar {x}}){\bar {x}}+{\frac {1}{2}}\sum \limits _{m=1}^{3}{\sum \limits _{n=1}^{3}{}{{\omega }^{m}}{{J}_{mn}}}{{\omega }^{n}}}}\\&mit\int _{}^{}{{{d}^{3}}x\rho ({\bar {x}}){\bar {x}}=0}\\\end{aligned}}

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\begin{aligned} T = \frac{1}{2} \int_{}^{} d^{3} x ρ (\bar{x}) {(\bar{V} + \bar{ω} \times \bar{x})}^{2} = \frac{1}{2} \int_{}^{} d^{3} x ρ (\bar{x}) V^{2} + (\bar{V} \times \bar{ω}) \int_{}^{} d^{3} x ρ (\bar{x}) \bar{x} + \frac{1}{2} \sum_{m = 1}^{3} \sum_{n = 1}^{3} ω^{m} J_{m n} ω^{n} \\ m i t \int_{}^{} d^{3} x ρ (\bar{x}) \bar{x} = 0 \end{aligned}

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Identifiers

$T$

$x$

$ρ$

$\bar{x}$

$\bar{V}$

$\bar{ω}$

$\bar{x}$

$x$

$ρ$

$\bar{x}$

$V$

$\bar{V}$

$\bar{ω}$

$x$

$ρ$

$\bar{x}$

$\bar{x}$

$m$

$n$

$ω$

$m$

$J_{m n}$

$ω$

$n$

$m$

$i$

$t$

$x$

$ρ$

$\bar{x}$

$\bar{x}$

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