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Display information for equation id:math.1346.37 on revision:1346

* Page found: Mechanik des starren Körpers (eq math.1346.37)

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TeX (original user input):

\begin{align}
  & {{J}_{mn}}\acute{\ }=\sum\limits_{l=1}^{3}{\sum\limits_{s=1}^{3}{{}}{{R}_{ml}}{{R}_{ns}}{{J}_{ls}}}=\sum\limits_{i=1}^{n}{{{m}_{i}}}\sum\limits_{l=1}^{3}{\sum\limits_{s=1}^{3}{{}}{{R}_{ml}}{{R}_{ns}}\left[ \left( \sum\limits_{t}{{{x}_{t}}{{^{(i)}}^{2}}} \right){{\delta }_{ls}}-{{x}_{l}}^{(i)}{{x}_{s}}^{(i)} \right]} \\ 
 & {{J}_{mn}}\acute{\ }=\sum\limits_{i=1}^{n}{{{m}_{i}}}\left[ \left( \sum\limits_{t}{{{x}_{t}}^{(i)}{{\acute{\ }}^{2}}} \right){{\delta }_{mn}}-{{x}_{m}}^{(i)}\acute{\ }{{x}_{n}}^{(i)}\acute{\ } \right] \\ 
\end{align}

TeX (checked):

{\begin{aligned}&{{J}_{mn}}{\acute {\ }}=\sum \limits _{l=1}^{3}{\sum \limits _{s=1}^{3}{}{{R}_{ml}}{{R}_{ns}}{{J}_{ls}}}=\sum \limits _{i=1}^{n}{{m}_{i}}\sum \limits _{l=1}^{3}{\sum \limits _{s=1}^{3}{}{{R}_{ml}}{{R}_{ns}}\left[\left(\sum \limits _{t}{{{x}_{t}}{{^{(i)}}^{2}}}\right){{\delta }_{ls}}-{{x}_{l}}^{(i)}{{x}_{s}}^{(i)}\right]}\\&{{J}_{mn}}{\acute {\ }}=\sum \limits _{i=1}^{n}{{m}_{i}}\left[\left(\sum \limits _{t}{{{x}_{t}}^{(i)}{{\acute {\ }}^{2}}}\right){{\delta }_{mn}}-{{x}_{m}}^{(i)}{\acute {\ }}{{x}_{n}}^{(i)}{\acute {\ }}\right]\\\end{aligned}}

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MathML (5.961 KB / 628 B) :

\begin{aligned} J_{m n} \overset{´}{} = \sum_{l = 1}^{3} \sum_{s = 1}^{3} R_{m l} R_{n s} J_{l s} = \sum_{i = 1}^{n} m_{i} \sum_{l = 1}^{3} \sum_{s = 1}^{3} R_{m l} R_{n s} [(\sum_{t} x_{t} {^{(i)}}^{2}) δ_{l s} - {x_{l}}^{(i)} {x_{s}}^{(i)}] \\ J_{m n} \overset{´}{} = \sum_{i = 1}^{n} m_{i} [(\sum_{t} {x_{t}}^{(i)} {\overset{´}{}}^{2}) δ_{m n} - {x_{m}}^{(i)} \overset{´}{} {x_{n}}^{(i)} \overset{´}{}] \end{aligned}

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Identifiers

$J_{m n}$

$\overset{´}{}$

$l$

$s$

$R_{m l}$

$R_{n s}$

$J_{l s}$

$i$

$n$

$m_{i}$

$l$

$s$

$R_{m l}$

$R_{n s}$

$t$

$x_{t}$

$i$

$δ_{l s}$

$x_{l}$

$i$

$x_{s}$

$i$

$J_{m n}$

$\overset{´}{}$

$i$

$n$

$m_{i}$

$t$

$x_{t}$

$i$

$\overset{´}{}$

$δ_{m n}$

$x_{m}$

$i$

$\overset{´}{}$

$x_{n}$

$i$

$\overset{´}{}$

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