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Display information for equation id:math.881.4 on revision:881
* Page found: Symplektische Struktur (eq math.881.4)
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Hash: 89988234531130158f3ada993a40b06d
TeX (original user input):
{{M}_{1}}\left( q,Q,t \right):p={{\partial }_{q}}{{M}_{1}},P={{\partial }_{Q}}{{M}_{1}}\Rightarrow \frac{\partial {{p}_{i}}}{\partial {{q}_{k}}}=\frac{{{\partial }^{2}}{{M}_{1}}}{\partial {{Q}_{k}}\partial {{q}_{i}}}=-\frac{\partial {{P}_{k}}}{\partial {{q}_{i}}}
TeX (checked):
{{M}_{1}}\left(q,Q,t\right):p={{\partial }_{q}}{{M}_{1}},P={{\partial }_{Q}}{{M}_{1}}\Rightarrow {\frac {\partial {{p}_{i}}}{\partial {{q}_{k}}}}={\frac {{{\partial }^{2}}{{M}_{1}}}{\partial {{Q}_{k}}\partial {{q}_{i}}}}=-{\frac {\partial {{P}_{k}}}{\partial {{q}_{i}}}}
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MathML (2.029 KB / 356 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mstyle><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>q</mi><mo>,</mo><mi>Q</mi><mo>,</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>:</mi><mi>p</mi><mo>=</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow></msub><msub><mi>M</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mi>P</mi><mo>=</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>Q</mi></mrow></msub><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"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></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><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><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>k</mi></mrow></msub><mi>∂</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow></mfrac></mrow><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><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><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow></mfrac></mrow></mrow></math>
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