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Display information for equation id:math.1957.58 on revision:1957
* Page found: Kanonische Transformationen (eq math.1957.58)
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Hash: 6af0eeff2e6e64c689890e4d156b5c52
TeX (original user input):
\frac{d}{dt}{{M}_{1}}=\frac{d}{dt}\left( {{M}_{2}}(\bar{q}(t),\bar{P}(t),t)-\sum\limits_{k}{{{P}_{k}}{{Q}_{k}}} \right)=\sum\limits_{k=1}^{f}{{}}\left( \frac{\partial {{M}_{2}}}{\partial {{q}_{k}}}{{{\dot{q}}}_{k}}+\frac{\partial {{M}_{2}}}{\partial {{P}_{k}}}{{{\dot{P}}}_{k}}-{{{\dot{P}}}_{k}}{{Q}_{k}}-{{P}_{k}}{{{\dot{Q}}}_{k}} \right)+\frac{\partial {{M}_{2}}}{\partial t}
TeX (checked):
{\frac {d}{dt}}{{M}_{1}}={\frac {d}{dt}}\left({{M}_{2}}({\bar {q}}(t),{\bar {P}}(t),t)-\sum \limits _{k}{{{P}_{k}}{{Q}_{k}}}\right)=\sum \limits _{k=1}^{f}{}\left({\frac {\partial {{M}_{2}}}{\partial {{q}_{k}}}}{{\dot {q}}_{k}}+{\frac {\partial {{M}_{2}}}{\partial {{P}_{k}}}}{{\dot {P}}_{k}}-{{\dot {P}}_{k}}{{Q}_{k}}-{{P}_{k}}{{\dot {Q}}_{k}}\right)+{\frac {\partial {{M}_{2}}}{\partial t}}
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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"><mfrac><mrow data-mjx-texclass="ORD"><mi>d</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi></mrow></mrow></mfrac></mrow><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>d</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>2</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 stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>P</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>−</mo><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></munder><mrow data-mjx-texclass="ORD"><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></munderover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</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>2</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>k</mi></mrow></msub></mrow></mrow></mfrac></mrow><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>k</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>2</mn></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow></mrow></mfrac></mrow><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>P</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo>−</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>P</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo>−</mo><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>Q</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><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>2</mn></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>t</mi></mrow></mrow></mfrac></mrow></mstyle></mrow></math>
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