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Display information for equation id:math.1325.40 on revision:1325

* Page found: Der Hamiltonsche kanonische Formalismus (eq math.1325.40)

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Die Hamiltonschen Gleichungen Eq: math.1948.14

Hash: d17cf80e4ce5910b45fc70f27d8b50ea

TeX (original user input):

\begin{align}
  & \frac{dH}{dt}=\frac{d}{dt}\left( \sum\limits_{k=1}^{f}{{}}\frac{\partial L}{\partial {{{\dot{q}}}_{k}}}{{{\dot{q}}}_{k}}-L \right)=\sum\limits_{k=1}^{f}{{}}\left( \frac{\partial H}{\partial {{q}_{k}}}{{{\dot{q}}}_{k}}+\frac{\partial H}{\partial {{p}_{k}}}{{{\dot{p}}}_{k}} \right)+\frac{\partial H}{\partial t}=\sum\limits_{k=1}^{f}{{}}\left( \frac{\partial H}{\partial {{q}_{k}}}\frac{\partial H}{\partial {{p}_{k}}}-\frac{\partial H}{\partial {{p}_{k}}}\frac{\partial H}{\partial {{q}_{k}}} \right)-\frac{\partial L}{\partial t}=0 \\ 
 & wegen\frac{\partial L}{\partial t}=0 \\ 
\end{align}

TeX (checked):

{\begin{aligned}&{\frac {dH}{dt}}={\frac {d}{dt}}\left(\sum \limits _{k=1}^{f}{}{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}{{\dot {q}}_{k}}-L\right)=\sum \limits _{k=1}^{f}{}\left({\frac {\partial H}{\partial {{q}_{k}}}}{{\dot {q}}_{k}}+{\frac {\partial H}{\partial {{p}_{k}}}}{{\dot {p}}_{k}}\right)+{\frac {\partial H}{\partial t}}=\sum \limits _{k=1}^{f}{}\left({\frac {\partial H}{\partial {{q}_{k}}}}{\frac {\partial H}{\partial {{p}_{k}}}}-{\frac {\partial H}{\partial {{p}_{k}}}}{\frac {\partial H}{\partial {{q}_{k}}}}\right)-{\frac {\partial L}{\partial t}}=0\\&wegen{\frac {\partial L}{\partial t}}=0\\\end{aligned}}

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\begin{aligned} \frac{d H}{d t} = \frac{d}{d t} (\sum_{k = 1}^{f} \frac{\partial L}{\partial {\dot{q}}_{k}} {\dot{q}}_{k} - L) = \sum_{k = 1}^{f} (\frac{\partial H}{\partial q_{k}} {\dot{q}}_{k} + \frac{\partial H}{\partial p_{k}} {\dot{p}}_{k}) + \frac{\partial H}{\partial t} = \sum_{k = 1}^{f} (\frac{\partial H}{\partial q_{k}} \frac{\partial H}{\partial p_{k}} - \frac{\partial H}{\partial p_{k}} \frac{\partial H}{\partial q_{k}}) - \frac{\partial L}{\partial t} = 0 \\ w e g e n \frac{\partial L}{\partial t} = 0 \end{aligned}

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Identifiers

$d$

$H$

$d$

$t$

$d$

$d$

$t$

$k$

$f$

$L$

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

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

$L$

$k$

$f$

$H$

$q_{k}$

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

$H$

$p_{k}$

${\dot{p}}_{k}$

$H$

$t$

$k$

$f$

$H$

$q_{k}$

$H$

$p_{k}$

$H$

$p_{k}$

$H$

$q_{k}$

$L$

$t$

$w$

$e$

$g$

$e$

$n$

$L$

$t$

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