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Display information for equation id:math.1410.9 on revision:1410

* Page found: Symmetrien und Erhaltungsgrößen (eq math.1410.9)

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Hash: 27caff2730774d82c82311da7ae0bc78

TeX (original user input):

\begin{align}
  & \frac{d}{ds}L(\bar{q}(s,t),\dot{\bar{q}}(s,t))=\sum\limits_{i=1}^{f}{\left( \frac{\partial L}{\partial {{q}_{i}}}\left( \frac{d{{q}_{i}}}{ds} \right)+\frac{\partial L}{\partial {{{\dot{q}}}_{i}}}{{\left( \frac{d{{{\dot{q}}}_{i}}}{ds} \right)}_{{}}} \right)=}0 \\ 
 & \Rightarrow \frac{d}{dt}I(\bar{q},\dot{\bar{q}})=\sum\limits_{i=1}^{f}{\frac{d}{dt}\left( \frac{\partial L}{\partial {{{\dot{q}}}_{i}}}{{\left( \frac{d}{ds}{{h}^{s}}({{q}_{i}}) \right)}_{s=0}} \right)=}\sum\limits_{i=1}^{f}{\left( \frac{d}{dt}\frac{\partial L}{\partial {{{\dot{q}}}_{i}}}\left( \frac{d{{q}_{i}}}{ds} \right)+\frac{\partial L}{\partial {{{\dot{q}}}_{i}}}\frac{d}{dt}{{\left( \frac{d{{q}_{i}}}{ds} \right)}_{{}}} \right)} \\ 
\end{align}

TeX (checked):

{\begin{aligned}&{\frac {d}{ds}}L({\bar {q}}(s,t),{\dot {\bar {q}}}(s,t))=\sum \limits _{i=1}^{f}{\left({\frac {\partial L}{\partial {{q}_{i}}}}\left({\frac {d{{q}_{i}}}{ds}}\right)+{\frac {\partial L}{\partial {{\dot {q}}_{i}}}}{{\left({\frac {d{{\dot {q}}_{i}}}{ds}}\right)}_{}}\right)=}0\\&\Rightarrow {\frac {d}{dt}}I({\bar {q}},{\dot {\bar {q}}})=\sum \limits _{i=1}^{f}{{\frac {d}{dt}}\left({\frac {\partial L}{\partial {{\dot {q}}_{i}}}}{{\left({\frac {d}{ds}}{{h}^{s}}({{q}_{i}})\right)}_{s=0}}\right)=}\sum \limits _{i=1}^{f}{\left({\frac {d}{dt}}{\frac {\partial L}{\partial {{\dot {q}}_{i}}}}\left({\frac {d{{q}_{i}}}{ds}}\right)+{\frac {\partial L}{\partial {{\dot {q}}_{i}}}}{\frac {d}{dt}}{{\left({\frac {d{{q}_{i}}}{ds}}\right)}_{}}\right)}\\\end{aligned}}

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\begin{aligned} \frac{d}{d s} L (\bar{q} (s, t), \dot{\bar{q}} (s, t)) = \sum_{i = 1}^{f} (\frac{\partial L}{\partial q_{i}} (\frac{d q_{i}}{d s}) + \frac{\partial L}{\partial {\dot{q}}_{i}} {(\frac{d {\dot{q}}_{i}}{d s})}_{}) = 0 \\ \Rightarrow \frac{d}{d t} I (\bar{q}, \dot{\bar{q}}) = \sum_{i = 1}^{f} \frac{d}{d t} (\frac{\partial L}{\partial {\dot{q}}_{i}} {(\frac{d}{d s} h^{s} (q_{i}))}_{s = 0}) = \sum_{i = 1}^{f} (\frac{d}{d t} \frac{\partial L}{\partial {\dot{q}}_{i}} (\frac{d q_{i}}{d s}) + \frac{\partial L}{\partial {\dot{q}}_{i}} \frac{d}{d t} {(\frac{d q_{i}}{d s})}_{}) \end{aligned}

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Identifiers

$d$

$d$

$s$

$L$

$\bar{q}$

$s$

$t$

$\dot{\bar{q}}$

$s$

$t$

$i$

$f$

$L$

$q_{i}$

$d$

$q_{i}$

$d$

$s$

$L$

${\dot{q}}_{i}$

$d$

${\dot{q}}_{i}$

$d$

$s$

$d$

$d$

$t$

$I$

$\bar{q}$

$\dot{\bar{q}}$

$i$

$f$

$d$

$d$

$t$

$L$

${\dot{q}}_{i}$

$d$

$d$

$s$

$h$

$s$

$q_{i}$

$s$

$i$

$f$

$d$

$d$

$t$

$L$

${\dot{q}}_{i}$

$d$

$q_{i}$

$d$

$s$

$L$

${\dot{q}}_{i}$

$d$

$d$

$t$

$d$

$q_{i}$

$d$

$s$

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