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Display information for equation id:math.1957.53 on revision:1957

* Page found: Kanonische Transformationen (eq math.1957.53)

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Kanonische Transformationen Eq: math.1957.53

Hash: be85ae5a0f94a239cea12c1b9976fd09

TeX (original user input):

0=\delta  \int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dtL}=\sum\limits_{k=1}^{f}{{}}\left. \left( {{P}_{k}}+\frac{\partial {{M}_{1}}}{\partial {{Q}_{k}}} \right)\delta {{Q}_{k}} \right|_{{{t}_{1}}}^{{{t}_{2}}}+\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt}\sum\limits_{k=1}^{f}{{}}\left\{ \left( {{{\dot{Q}}}_{k}}(t)-\frac{\partial \bar{H}(\bar{Q},\bar{P},t)}{\partial {{P}_{k}}} \right)\delta {{P}_{k}}-\left( {{{\dot{P}}}_{k}}(t)+\frac{\partial \bar{H}(\bar{Q},\bar{P},t)}{\partial {{Q}_{k}}} \right)\delta {{Q}_{k}} \right\}

TeX (checked):

0=\delta \int \limits _{{t}_{1}}^{{t}_{2}}{dtL}=\sum \limits _{k=1}^{f}{}\left.\left({{P}_{k}}+{\frac {\partial {{M}_{1}}}{\partial {{Q}_{k}}}}\right)\delta {{Q}_{k}}\right|_{{t}_{1}}^{{t}_{2}}+\int \limits _{{t}_{1}}^{{t}_{2}}{dt}\sum \limits _{k=1}^{f}{}\left\{\left({{\dot {Q}}_{k}}(t)-{\frac {\partial {\bar {H}}({\bar {Q}},{\bar {P}},t)}{\partial {{P}_{k}}}}\right)\delta {{P}_{k}}-\left({{\dot {P}}_{k}}(t)+{\frac {\partial {\bar {H}}({\bar {Q}},{\bar {P}},t)}{\partial {{Q}_{k}}}}\right)\delta {{Q}_{k}}\right\}

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0 = δ \int_{t_{1}}^{t_{2}} d t L = \sum_{k = 1}^{f} {(P_{k} + \frac{\partial M_{1}}{\partial Q_{k}}) δ Q_{k} |}_{t_{1}}^{t_{2}} + \int_{t_{1}}^{t_{2}} d t \sum_{k = 1}^{f} {({\dot{Q}}_{k} (t) - \frac{\partial \bar{H} (\bar{Q}, \bar{P}, t)}{\partial P_{k}}) δ P_{k} - ({\dot{P}}_{k} (t) + \frac{\partial \bar{H} (\bar{Q}, \bar{P}, t)}{\partial Q_{k}}) δ Q_{k}}

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Identifiers

$δ$

$t_{1}$

$t_{2}$

$t$

$L$

$k$

$f$

$P_{k}$

$M_{1}$

$Q_{k}$

$δ$

$Q_{k}$

$t_{1}$

$t_{2}$

$t_{1}$

$t_{2}$

$t$

$k$

$f$

${\dot{Q}}_{k}$

$t$

$\bar{H}$

$\bar{Q}$

$\bar{P}$

$t$

$P_{k}$

$δ$

$P_{k}$

${\dot{P}}_{k}$

$t$

$\bar{H}$

$\bar{Q}$

$\bar{P}$

$t$

$Q_{k}$

$δ$

$Q_{k}$

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