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Display information for equation id:math.1256.177 on revision:1256

* Page found: Das d'Alembertsche Prinzip (eq math.1256.177)

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Normalschwingungen Eq: math.1515.40

Hash: b4daeb4696a2dbe9161aa0bae79c10e7

TeX (original user input):

\begin{align}
  & L=T-V=\frac{1}{2}\left( \sum\limits_{j,k}{{{T}_{jk}}}{{{\dot{q}}}_{j}}{{{\dot{q}}}_{k}}-\sum\limits_{j,k}{{{V}_{jk}}}{{q}_{j}}{{q}_{k}} \right) \\
 & L=\frac{1}{2}\left( \sum\limits_{a,b}{\left( \sum\limits_{j,k}{{{A}_{j}}^{b}{{T}_{jk}}{{A}_{k}}^{a}{{{\dot{Q}}}_{a}}{{{\dot{Q}}}_{b}}-\sum\limits_{j,k}{{{A}_{j}}^{b}{{V}_{jk}}{{A}_{k}}^{a}{{Q}_{a}}{{Q}_{b}}}} \right)} \right) \\
 & \sum\limits_{j,k}{{{A}_{j}}^{b}{{T}_{jk}}{{A}_{k}}^{a}={{\delta }_{ab}}} \\
 & \sum\limits_{j,k}{{{A}_{j}}^{b}{{V}_{jk}}{{A}_{k}}^{a}={{\omega }_{a}}^{2}{{\delta }_{ab}}} \\
 & L=\frac{1}{2}\left( \sum\limits_{a}{\left( {{{\dot{Q}}}_{a}}^{2}-{{\omega }_{a}}^{2}{{Q}_{a}}^{2} \right)} \right) \\
\end{align}

TeX (checked):

{\begin{aligned}&L=T-V={\frac {1}{2}}\left(\sum \limits _{j,k}{{T}_{jk}}{{\dot {q}}_{j}}{{\dot {q}}_{k}}-\sum \limits _{j,k}{{V}_{jk}}{{q}_{j}}{{q}_{k}}\right)\\&L={\frac {1}{2}}\left(\sum \limits _{a,b}{\left(\sum \limits _{j,k}{{{A}_{j}}^{b}{{T}_{jk}}{{A}_{k}}^{a}{{\dot {Q}}_{a}}{{\dot {Q}}_{b}}-\sum \limits _{j,k}{{{A}_{j}}^{b}{{V}_{jk}}{{A}_{k}}^{a}{{Q}_{a}}{{Q}_{b}}}}\right)}\right)\\&\sum \limits _{j,k}{{{A}_{j}}^{b}{{T}_{jk}}{{A}_{k}}^{a}={{\delta }_{ab}}}\\&\sum \limits _{j,k}{{{A}_{j}}^{b}{{V}_{jk}}{{A}_{k}}^{a}={{\omega }_{a}}^{2}{{\delta }_{ab}}}\\&L={\frac {1}{2}}\left(\sum \limits _{a}{\left({{\dot {Q}}_{a}}^{2}-{{\omega }_{a}}^{2}{{Q}_{a}}^{2}\right)}\right)\\\end{aligned}}

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\begin{aligned} L = T - V = \frac{1}{2} (\sum_{j, k} T_{j k} {\dot{q}}_{j} {\dot{q}}_{k} - \sum_{j, k} V_{j k} q_{j} q_{k}) \\ L = \frac{1}{2} (\sum_{a, b} (\sum_{j, k} {A_{j}}^{b} T_{j k} {A_{k}}^{a} {\dot{Q}}_{a} {\dot{Q}}_{b} - \sum_{j, k} {A_{j}}^{b} V_{j k} {A_{k}}^{a} Q_{a} Q_{b})) \\ \sum_{j, k} {A_{j}}^{b} T_{j k} {A_{k}}^{a} = δ_{a b} \\ \sum_{j, k} {A_{j}}^{b} V_{j k} {A_{k}}^{a} = {ω_{a}}^{2} δ_{a b} \\ L = \frac{1}{2} (\sum_{a} ({\dot{Q}}_{a}^{2} - {ω_{a}}^{2} {Q_{a}}^{2})) \end{aligned}

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Identifiers

$L$

$T$

$V$

$j$

$k$

$T_{j k}$

${\dot{q}}_{j}$

${\dot{q}}_{k}$

$j$

$k$

$V_{j k}$

$q_{j}$

$q_{k}$

$L$

$a$

$b$

$j$

$k$

$A_{j}$

$b$

$T_{j k}$

$A_{k}$

$a$

${\dot{Q}}_{a}$

${\dot{Q}}_{b}$

$j$

$k$

$A_{j}$

$b$

$V_{j k}$

$A_{k}$

$a$

$Q_{a}$

$Q_{b}$

$j$

$k$

$A_{j}$

$b$

$T_{j k}$

$A_{k}$

$a$

$δ_{a b}$

$j$

$k$

$A_{j}$

$b$

$V_{j k}$

$A_{k}$

$a$

$ω_{a}$

$δ_{a b}$

$L$

$a$

${\dot{Q}}_{a}$

$ω_{a}$

$Q_{a}$

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