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Display information for equation id:math.1322.74 on revision:1322

* Page found: Das Hamiltonsche Prinzip (eq math.1322.74)

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Eichtransformation der Lagrangefunktion Eq: math.1905.22

Hash: 8c49ffa7434e9acb802163e339e3b040

TeX (original user input):

\begin{align}
  & \frac{\partial L\acute{\ }}{\partial {{q}_{k}}}-\frac{d}{dt}\frac{\partial L\acute{\ }}{\partial {{{\dot{q}}}_{k}}}=\frac{\partial L}{\partial {{q}_{k}}}+\frac{\partial }{\partial {{q}_{k}}}\left( \sum\limits_{l=1}^{f}{\frac{\partial M}{\partial {{q}_{l}}}{{{\dot{q}}}_{l}}+\frac{\partial M}{\partial t}} \right)-\frac{d}{dt}\frac{\partial L}{\partial {{{\dot{q}}}_{k}}}-\frac{d}{dt}\frac{\partial }{\partial {{{\dot{q}}}_{k}}}\left( \sum\limits_{l=1}^{f}{\frac{\partial M}{\partial {{q}_{l}}}{{{\dot{q}}}_{l}}+\frac{\partial M}{\partial t}} \right) \\
 & =\frac{\partial L}{\partial {{q}_{k}}}-\frac{d}{dt}\frac{\partial L}{\partial {{{\dot{q}}}_{k}}}+\frac{\partial }{\partial {{q}_{k}}}\frac{dM}{dt}-\frac{d}{dt}\frac{\partial M}{\partial {{q}_{k}}}=\frac{\partial L}{\partial {{q}_{k}}}-\frac{d}{dt}\frac{\partial L}{\partial {{{\dot{q}}}_{k}}} \\
\end{align}

TeX (checked):

{\begin{aligned}&{\frac {\partial L{\acute {\ }}}{\partial {{q}_{k}}}}-{\frac {d}{dt}}{\frac {\partial L{\acute {\ }}}{\partial {{\dot {q}}_{k}}}}={\frac {\partial L}{\partial {{q}_{k}}}}+{\frac {\partial }{\partial {{q}_{k}}}}\left(\sum \limits _{l=1}^{f}{{\frac {\partial M}{\partial {{q}_{l}}}}{{\dot {q}}_{l}}+{\frac {\partial M}{\partial t}}}\right)-{\frac {d}{dt}}{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}-{\frac {d}{dt}}{\frac {\partial }{\partial {{\dot {q}}_{k}}}}\left(\sum \limits _{l=1}^{f}{{\frac {\partial M}{\partial {{q}_{l}}}}{{\dot {q}}_{l}}+{\frac {\partial M}{\partial t}}}\right)\\&={\frac {\partial L}{\partial {{q}_{k}}}}-{\frac {d}{dt}}{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}+{\frac {\partial }{\partial {{q}_{k}}}}{\frac {dM}{dt}}-{\frac {d}{dt}}{\frac {\partial M}{\partial {{q}_{k}}}}={\frac {\partial L}{\partial {{q}_{k}}}}-{\frac {d}{dt}}{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}\\\end{aligned}}

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\begin{aligned} \frac{\partial L \overset{´}{}}{\partial q_{k}} - \frac{d}{d t} \frac{\partial L \overset{´}{}}{\partial {\dot{q}}_{k}} = \frac{\partial L}{\partial q_{k}} + \frac{\partial}{\partial q_{k}} (\sum_{l = 1}^{f} \frac{\partial M}{\partial q_{l}} {\dot{q}}_{l} + \frac{\partial M}{\partial t}) - \frac{d}{d t} \frac{\partial L}{\partial {\dot{q}}_{k}} - \frac{d}{d t} \frac{\partial}{\partial {\dot{q}}_{k}} (\sum_{l = 1}^{f} \frac{\partial M}{\partial q_{l}} {\dot{q}}_{l} + \frac{\partial M}{\partial t}) \\ = \frac{\partial L}{\partial q_{k}} - \frac{d}{d t} \frac{\partial L}{\partial {\dot{q}}_{k}} + \frac{\partial}{\partial q_{k}} \frac{d M}{d t} - \frac{d}{d t} \frac{\partial M}{\partial q_{k}} = \frac{\partial L}{\partial q_{k}} - \frac{d}{d t} \frac{\partial L}{\partial {\dot{q}}_{k}} \end{aligned}

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Identifiers

$L$

$\overset{´}{}$

$q_{k}$

$d$

$d$

$t$

$L$

$\overset{´}{}$

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

$L$

$q_{k}$

$q_{k}$

$l$

$f$

$M$

$q_{l}$

${\dot{q}}_{l}$

$M$

$t$

$d$

$d$

$t$

$L$

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

$d$

$d$

$t$

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

$l$

$f$

$M$

$q_{l}$

${\dot{q}}_{l}$

$M$

$t$

$L$

$q_{k}$

$d$

$d$

$t$

$L$

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

$q_{k}$

$d$

$M$

$d$

$t$

$d$

$d$

$t$

$M$

$q_{k}$

$L$

$q_{k}$

$d$

$d$

$t$

$L$

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

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