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Display information for equation id:math.2010.69 on revision:2010

* Page found: Kinetische Energie und Trägheitstensor (eq math.2010.69)

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Kinetische Energie und Trägheitstensor Eq: math.2016.69

Hash: 02cb5092c87aff684b5ecf67baf2d907

TeX (original user input):

\begin{align}
  & {{J}_{mn}}\acute{\ }=\int_{{}}^{{}}{{{d}^{3}}x}\rho (\bar{x})\left[ \left( \sum\limits_{t}{{{\left( {{x}_{t}}+{{a}_{t}} \right)}^{2}}} \right){{\delta }_{mn}}-\left( {{x}_{m}}+{{a}_{m}} \right)\left( {{x}_{n}}+{{a}_{n}} \right) \right] \\
 & {{J}_{mn}}\acute{\ }=\int_{{}}^{{}}{{{d}^{3}}x}\rho (\bar{x})\left[ \left( \sum\limits_{t}{\left[ {{\left( {{x}_{t}} \right)}^{2}}+2\left( {{a}_{t}}{{x}_{t}} \right)+{{a}_{t}}^{2} \right]} \right){{\delta }_{mn}}-{{x}_{m}}{{x}_{n}}-{{x}_{m}}{{a}_{n}}-{{x}_{n}}{{a}_{m}}-{{a}_{m}}{{a}_{n}} \right] \\
 & \int_{{}}^{{}}{{{d}^{3}}x}\rho (\bar{x})\sum\limits_{t}{\left( {{a}_{t}}{{x}_{t}} \right)}=\int_{{}}^{{}}{{{d}^{3}}x}\rho (\bar{x})\left( {{x}_{m}}{{a}_{n}}+{{x}_{n}}{{a}_{m}} \right)=0\quad wegen\ \int_{{}}^{{}}{{{d}^{3}}x}\rho (\bar{x})\bar{x}=0 \\
\end{align}

TeX (checked):

{\begin{aligned}&{{J}_{mn}}{\acute {\ }}=\int _{}^{}{{{d}^{3}}x}\rho ({\bar {x}})\left[\left(\sum \limits _{t}{{\left({{x}_{t}}+{{a}_{t}}\right)}^{2}}\right){{\delta }_{mn}}-\left({{x}_{m}}+{{a}_{m}}\right)\left({{x}_{n}}+{{a}_{n}}\right)\right]\\&{{J}_{mn}}{\acute {\ }}=\int _{}^{}{{{d}^{3}}x}\rho ({\bar {x}})\left[\left(\sum \limits _{t}{\left[{{\left({{x}_{t}}\right)}^{2}}+2\left({{a}_{t}}{{x}_{t}}\right)+{{a}_{t}}^{2}\right]}\right){{\delta }_{mn}}-{{x}_{m}}{{x}_{n}}-{{x}_{m}}{{a}_{n}}-{{x}_{n}}{{a}_{m}}-{{a}_{m}}{{a}_{n}}\right]\\&\int _{}^{}{{{d}^{3}}x}\rho ({\bar {x}})\sum \limits _{t}{\left({{a}_{t}}{{x}_{t}}\right)}=\int _{}^{}{{{d}^{3}}x}\rho ({\bar {x}})\left({{x}_{m}}{{a}_{n}}+{{x}_{n}}{{a}_{m}}\right)=0\quad wegen\ \int _{}^{}{{{d}^{3}}x}\rho ({\bar {x}}){\bar {x}}=0\\\end{aligned}}

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\begin{aligned} J_{m n} \overset{´}{} = \int_{}^{} d^{3} x ρ (\bar{x}) [(\sum_{t} {(x_{t} + a_{t})}^{2}) δ_{m n} - (x_{m} + a_{m}) (x_{n} + a_{n})] \\ J_{m n} \overset{´}{} = \int_{}^{} d^{3} x ρ (\bar{x}) [(\sum_{t} [{(x_{t})}^{2} + 2 (a_{t} x_{t}) + {a_{t}}^{2}]) δ_{m n} - x_{m} x_{n} - x_{m} a_{n} - x_{n} a_{m} - a_{m} a_{n}] \\ \int_{}^{} d^{3} x ρ (\bar{x}) \sum_{t} (a_{t} x_{t}) = \int_{}^{} d^{3} x ρ (\bar{x}) (x_{m} a_{n} + x_{n} a_{m}) = 0 w e g e n \int_{}^{} d^{3} x ρ (\bar{x}) \bar{x} = 0 \end{aligned}

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Identifiers

$J_{m n}$

$\overset{´}{}$

$x$

$ρ$

$\bar{x}$

$t$

$x_{t}$

$a_{t}$

$δ_{m n}$

$x_{m}$

$a_{m}$

$x_{n}$

$a_{n}$

$J_{m n}$

$\overset{´}{}$

$x$

$ρ$

$\bar{x}$

$t$

$x_{t}$

$a_{t}$

$x_{t}$

$a_{t}$

$δ_{m n}$

$x_{m}$

$x_{n}$

$x_{m}$

$a_{n}$

$x_{n}$

$a_{m}$

$a_{m}$

$a_{n}$

$x$

$ρ$

$\bar{x}$

$t$

$a_{t}$

$x_{t}$

$x$

$ρ$

$\bar{x}$

$x_{m}$

$a_{n}$

$x_{n}$

$a_{m}$

$w$

$e$

$g$

$e$

$n$

$x$

$ρ$

$\bar{x}$

$\bar{x}$

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