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Display information for equation id:math.1957.42 on revision:1957

* Page found: Kanonische Transformationen (eq math.1957.42)

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Kanonische Transformationen Eq: math.1957.42

Hash: fd2a5be16f43e45e0d802529695636d4

TeX (original user input):

\begin{align}
  & {{p}_{k}}=\frac{\partial {{M}_{1}}(\bar{q},\bar{Q},t)}{\partial {{q}_{k}}}\Rightarrow {{Q}_{j}}(\bar{q},\bar{p},t) \\ 
 & Bedingung:\det \left( \frac{{{\partial }^{2}}{{M}_{1}}}{\partial {{q}_{k}}\partial {{Q}_{j}}} \right)\ne 0 \\ 
 & {{P}_{k}}=-\frac{\partial {{M}_{1}}(\bar{q},\bar{Q},t)}{\partial {{Q}_{k}}}=-\frac{\partial {{M}_{1}}(\bar{q},\bar{Q}(\bar{q},\bar{p},t),t)}{\partial {{Q}_{k}}}={{P}_{k}}(\bar{q},\bar{p},t) \\ 
\end{align}

TeX (checked):

{\begin{aligned}&{{p}_{k}}={\frac {\partial {{M}_{1}}({\bar {q}},{\bar {Q}},t)}{\partial {{q}_{k}}}}\Rightarrow {{Q}_{j}}({\bar {q}},{\bar {p}},t)\\&Bedingung:\det \left({\frac {{{\partial }^{2}}{{M}_{1}}}{\partial {{q}_{k}}\partial {{Q}_{j}}}}\right)\neq 0\\&{{P}_{k}}=-{\frac {\partial {{M}_{1}}({\bar {q}},{\bar {Q}},t)}{\partial {{Q}_{k}}}}=-{\frac {\partial {{M}_{1}}({\bar {q}},{\bar {Q}}({\bar {q}},{\bar {p}},t),t)}{\partial {{Q}_{k}}}}={{P}_{k}}({\bar {q}},{\bar {p}},t)\\\end{aligned}}

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\begin{aligned} p_{k} = \frac{\partial M_{1} (\bar{q}, \bar{Q}, t)}{\partial q_{k}} \Rightarrow Q_{j} (\bar{q}, \bar{p}, t) \\ B e d i n g u n g : \det (\frac{\partial^{2} M_{1}}{\partial q_{k} \partial Q_{j}}) \neq 0 \\ P_{k} = - \frac{\partial M_{1} (\bar{q}, \bar{Q}, t)}{\partial Q_{k}} = - \frac{\partial M_{1} (\bar{q}, \bar{Q} (\bar{q}, \bar{p}, t), t)}{\partial Q_{k}} = P_{k} (\bar{q}, \bar{p}, t) \end{aligned}

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Identifiers

$p_{k}$

$M_{1}$

$\bar{q}$

$\bar{Q}$

$t$

$q_{k}$

$Q_{j}$

$\bar{q}$

$\bar{p}$

$t$

$B$

$e$

$d$

$i$

$n$

$g$

$u$

$n$

$g$

$M_{1}$

$q_{k}$

$Q_{j}$

$P_{k}$

$M_{1}$

$\bar{q}$

$\bar{Q}$

$t$

$Q_{k}$

$M_{1}$

$\bar{q}$

$\bar{Q}$

$\bar{q}$

$\bar{p}$

$t$

$t$

$Q_{k}$

$P_{k}$

$\bar{q}$

$\bar{p}$

$t$

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