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Display information for equation id:math.1321.43 on revision:1321

* Page found: Das Hamiltonsche Prinzip (eq math.1321.43)

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Das hamiltonsche Wirkungsprinzip Eq: math.1898.3

Hash: d0270c87e86ffee120ae55832276e8f5

TeX (original user input):

\begin{align}
  & \delta W=0 \\
 & \delta W=\delta \int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt}F=\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt}\sum\limits_{k=1}^{f}{{}}\left\{ \frac{\partial L}{\partial {{q}_{k}}}\delta {{q}_{k}}(t)+\frac{\partial L}{\partial {{{\dot{q}}}_{k}}}\frac{d}{dt}\delta {{q}_{k}}(t) \right\} \\
 & \delta W=\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt}\sum\limits_{k=1}^{f}{{}}\left\{ \frac{\partial L}{\partial {{q}_{k}}}-\frac{d}{dt}\frac{\partial L}{\partial {{{\dot{q}}}_{k}}} \right\}\delta {{q}_{k}}(t)=0 \\
\end{align}

TeX (checked):

{\begin{aligned}&\delta W=0\\&\delta W=\delta \int \limits _{{t}_{1}}^{{t}_{2}}{dt}F=\int \limits _{{t}_{1}}^{{t}_{2}}{dt}\sum \limits _{k=1}^{f}{}\left\{{\frac {\partial L}{\partial {{q}_{k}}}}\delta {{q}_{k}}(t)+{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}{\frac {d}{dt}}\delta {{q}_{k}}(t)\right\}\\&\delta W=\int \limits _{{t}_{1}}^{{t}_{2}}{dt}\sum \limits _{k=1}^{f}{}\left\{{\frac {\partial L}{\partial {{q}_{k}}}}-{\frac {d}{dt}}{\frac {\partial L}{\partial {{\dot {q}}_{k}}}}\right\}\delta {{q}_{k}}(t)=0\\\end{aligned}}

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\begin{aligned} δ W = 0 \\ δ W = δ \int_{t_{1}}^{t_{2}} d t F = \int_{t_{1}}^{t_{2}} d t \sum_{k = 1}^{f} {\frac{\partial L}{\partial q_{k}} δ q_{k} (t) + \frac{\partial L}{\partial {\dot{q}}_{k}} \frac{d}{d t} δ q_{k} (t)} \\ δ W = \int_{t_{1}}^{t_{2}} d t \sum_{k = 1}^{f} {\frac{\partial L}{\partial q_{k}} - \frac{d}{d t} \frac{\partial L}{\partial {\dot{q}}_{k}}} δ q_{k} (t) = 0 \end{aligned}

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Identifiers

$δ$

$W$

$δ$

$W$

$δ$

$t_{1}$

$t_{2}$

$t$

$F$

$t_{1}$

$t_{2}$

$t$

$k$

$f$

$L$

$q_{k}$

$δ$

$q_{k}$

$t$

$L$

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

$d$

$d$

$t$

$δ$

$q_{k}$

$t$

$δ$

$W$

$t_{1}$

$t_{2}$

$t$

$k$

$f$

$L$

$q_{k}$

$d$

$d$

$t$

$L$

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

$δ$

$q_{k}$

$t$

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