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Display information for equation id:math.1326.114 on revision:1326

* Page found: Der Hamiltonsche kanonische Formalismus (eq math.1326.114)

Occurrences on the following pages:

Kanonische Transformationen Eq: math.1957.47

Hash: d71f2c1a9093958edd1ae937b5343408

TeX (original user input):

\begin{align}
  & \delta \int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt}\left\{ \sum\limits_{k=1}^{f}{{}}{{p}_{k}}{{{\dot{q}}}_{k}}(t)-H(\bar{Q},\bar{P},t) \right\}=0 \\ 
 & \Leftrightarrow \delta \int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt}\left\{ \sum\limits_{k=1}^{f}{{}}{{P}_{k}}{{{\dot{Q}}}_{k}}(t)-\bar{H}(\bar{Q},\bar{P},t)+\frac{d}{dt}{{M}_{1}} \right\}=0 \\ 
 & =\delta \int\limits_{{{t}_{1}}}^{{{t}_{2}}}{dt}\left\{ \sum\limits_{k=1}^{f}{{}}{{P}_{k}}{{{\dot{Q}}}_{k}}(t)-\bar{H}(\bar{Q},\bar{P},t) \right\}+\delta \left\{ {{M}_{1}}(q({{t}_{2}}),Q({{t}_{2}}),{{t}_{2}})-{{M}_{1}}(q({{t}_{1}}),Q({{t}_{1}}),{{t}_{1}}) \right\} \\ 
\end{align}

TeX (checked):

{\begin{aligned}&\delta \int \limits _{{t}_{1}}^{{t}_{2}}{dt}\left\{\sum \limits _{k=1}^{f}{}{{p}_{k}}{{\dot {q}}_{k}}(t)-H({\bar {Q}},{\bar {P}},t)\right\}=0\\&\Leftrightarrow \delta \int \limits _{{t}_{1}}^{{t}_{2}}{dt}\left\{\sum \limits _{k=1}^{f}{}{{P}_{k}}{{\dot {Q}}_{k}}(t)-{\bar {H}}({\bar {Q}},{\bar {P}},t)+{\frac {d}{dt}}{{M}_{1}}\right\}=0\\&=\delta \int \limits _{{t}_{1}}^{{t}_{2}}{dt}\left\{\sum \limits _{k=1}^{f}{}{{P}_{k}}{{\dot {Q}}_{k}}(t)-{\bar {H}}({\bar {Q}},{\bar {P}},t)\right\}+\delta \left\{{{M}_{1}}(q({{t}_{2}}),Q({{t}_{2}}),{{t}_{2}})-{{M}_{1}}(q({{t}_{1}}),Q({{t}_{1}}),{{t}_{1}})\right\}\\\end{aligned}}

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\begin{aligned} δ \int_{t_{1}}^{t_{2}} d t {\sum_{k = 1}^{f} p_{k} {\dot{q}}_{k} (t) - H (\bar{Q}, \bar{P}, t)} = 0 \\ \Leftrightarrow δ \int_{t_{1}}^{t_{2}} d t {\sum_{k = 1}^{f} P_{k} {\dot{Q}}_{k} (t) - \bar{H} (\bar{Q}, \bar{P}, t) + \frac{d}{d t} M_{1}} = 0 \\ = δ \int_{t_{1}}^{t_{2}} d t {\sum_{k = 1}^{f} P_{k} {\dot{Q}}_{k} (t) - \bar{H} (\bar{Q}, \bar{P}, t)} + δ {M_{1} (q (t_{2}), Q (t_{2}), t_{2}) - M_{1} (q (t_{1}), Q (t_{1}), t_{1})} \end{aligned}

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Identifiers

$δ$

$t_{1}$

$t_{2}$

$t$

$k$

$f$

$p_{k}$

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

$t$

$H$

$\bar{Q}$

$\bar{P}$

$t$

$δ$

$t_{1}$

$t_{2}$

$t$

$k$

$f$

$P_{k}$

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

$t$

$\bar{H}$

$\bar{Q}$

$\bar{P}$

$t$

$d$

$d$

$t$

$M_{1}$

$δ$

$t_{1}$

$t_{2}$

$t$

$k$

$f$

$P_{k}$

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

$t$

$\bar{H}$

$\bar{Q}$

$\bar{P}$

$t$

$δ$

$M_{1}$

$q$

$t_{2}$

$Q$

$t_{2}$

$t_{2}$

$M_{1}$

$q$

$t_{1}$

$Q$

$t_{1}$

$t_{1}$

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