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Display information for equation id:math.1350.34 on revision:1350

* Page found: Mechanik des starren Körpers (eq math.1350.34)

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Kinetische Energie und Trägheitstensor Eq: math.2016.29

Hash: 1740dc251569361057a6c0a44af58302

TeX (original user input):

\begin{align}
  & {{x}_{m}}\acute{\ }=\sum\limits_{n=1}^{3}{{{R}_{mn}}{{x}_{n}}} \\
 & \Rightarrow \sum\limits_{t}{{{x}_{t}}{{\acute{\ }}^{2}}}=\sum\limits_{t}{\sum\limits_{l}{\sum\limits_{s}{{{R}_{tl}}{{R}_{ts}}{{x}_{l}}{{x}_{s}}}=}\sum\limits_{l}{\sum\limits_{s}{\left( \sum\limits_{t}{{}}{{R}_{lt}}^{T}{{R}_{ts}} \right){{x}_{l}}{{x}_{s}}}=\sum\limits_{l}{\sum\limits_{s}{{{\delta }_{ls}}{{x}_{l}}{{x}_{s}}}=\sum\limits_{l}{{{x}_{l}}^{2}}}}} \\
\end{align}

TeX (checked):

{\begin{aligned}&{{x}_{m}}{\acute {\ }}=\sum \limits _{n=1}^{3}{{{R}_{mn}}{{x}_{n}}}\\&\Rightarrow \sum \limits _{t}{{{x}_{t}}{{\acute {\ }}^{2}}}=\sum \limits _{t}{\sum \limits _{l}{\sum \limits _{s}{{{R}_{tl}}{{R}_{ts}}{{x}_{l}}{{x}_{s}}}=}\sum \limits _{l}{\sum \limits _{s}{\left(\sum \limits _{t}{}{{R}_{lt}}^{T}{{R}_{ts}}\right){{x}_{l}}{{x}_{s}}}=\sum \limits _{l}{\sum \limits _{s}{{{\delta }_{ls}}{{x}_{l}}{{x}_{s}}}=\sum \limits _{l}{{{x}_{l}}^{2}}}}}\\\end{aligned}}

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\begin{matrix} x_{m} \overset{´}{} = \sum_{n = 1}^{3} R_{m n} x_{n} \\ \Rightarrow \sum_{t} x_{t} {\overset{´}{}}^{2} = \sum_{t} \sum_{l} \sum_{s} R_{t l} R_{t s} x_{l} x_{s} = \sum_{l} \sum_{s} (\sum_{t} {R_{l t}}^{T} R_{t s}) x_{l} x_{s} = \sum_{l} \sum_{s} δ_{l s} x_{l} x_{s} = \sum_{l} {x_{l}}^{2} \end{matrix}

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Identifiers

$x_{m}$

$\overset{´}{}$

$n$

$R_{m n}$

$x_{n}$

$t$

$x_{t}$

$\overset{´}{}$

$t$

$l$

$s$

$R_{t l}$

$R_{t s}$

$x_{l}$

$x_{s}$

$l$

$s$

$t$

$R_{l t}$

$T$

$R_{t s}$

$x_{l}$

$x_{s}$

$l$

$s$

$δ_{l s}$

$x_{l}$

$x_{s}$

$l$

$x_{l}$

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