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Display information for equation id:math.1326.133 on revision:1326
* Page found: Der Hamiltonsche kanonische Formalismus (eq math.1326.133)
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Hash: a04b24768811607decc73c80527c7570
TeX (original user input):
\begin{align}
& {{M}_{1}}(\bar{q},\bar{Q},t)=\sum\limits_{j=1}^{f}{{}}{{q}_{j}}{{Q}_{j}} \\
& \Rightarrow {{p}_{j}}=\frac{\partial {{M}_{1}}}{\partial {{q}_{j}}}=-{{Q}_{j}} \\
& {{P}_{j}}=-\frac{\partial {{M}_{1}}}{\partial {{Q}_{j}}}={{q}_{j}} \\
& \left( \bar{q},\bar{p} \right)\to \left( \bar{P},-\bar{Q} \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&{{M}_{1}}({\bar {q}},{\bar {Q}},t)=\sum \limits _{j=1}^{f}{}{{q}_{j}}{{Q}_{j}}\\&\Rightarrow {{p}_{j}}={\frac {\partial {{M}_{1}}}{\partial {{q}_{j}}}}=-{{Q}_{j}}\\&{{P}_{j}}=-{\frac {\partial {{M}_{1}}}{\partial {{Q}_{j}}}}={{q}_{j}}\\&\left({\bar {q}},{\bar {p}}\right)\to \left({\bar {P}},-{\bar {Q}}\right)\\\end{aligned}}
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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>Q</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>j</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></munderover><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo>=</mo><mo>−</mo><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo>=</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo accent="false">→</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>P</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>Q</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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