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Display information for equation id:math.1965.14 on revision:1965
* Page found: Symplektische Struktur des Phasenraums (eq math.1965.14)
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Hash: 639e0381264653111c9c0d7180197b82
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\begin{align}
& {{M}_{4}}(\bar{p},\bar{P},t)={{M}_{1}}(\bar{q},\bar{Q},t)-\sum\limits_{j=1}^{f}{{}}\left( \frac{\partial {{M}_{1}}}{\partial {{Q}_{j}}}{{Q}_{j}}+\frac{\partial {{M}_{1}}}{\partial {{q}_{j}}}{{q}_{j}} \right) \\
& \Rightarrow {{q}_{j}}=-\frac{\partial {{M}_{4}}}{\partial {{p}_{j}}} \\
& {{Q}_{j}}=\frac{\partial {{M}_{1}}}{\partial {{P}_{j}}}={{q}_{j}} \\
& \Rightarrow \frac{\partial {{q}_{j}}}{\partial {{P}_{k}}}=\frac{{{\partial }^{2}}{{M}_{1}}}{\partial {{P}_{k}}\partial {{p}_{j}}}=-\frac{\partial {{Q}_{k}}}{\partial {{p}_{j}}} \\
\end{align}
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