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Display information for equation id:math.1989.7 on revision:1989
* Page found: Hamilton-Jacobische Differenzialgleichung (eq math.1989.7)
(force rerendering)Occurrences on the following pages:
Hash: a729390350c8e87f92346d72ddd576fa
TeX (original user input):
\begin{align}
& {{{\dot{P}}}_{k}}=-\frac{\partial H}{\partial {{Q}_{k}}}\equiv 0\Rightarrow {{P}_{k}}={{\alpha }_{k}}=cons \\
& {{{\dot{Q}}}_{k}}=\frac{\partial \bar{H}}{\partial {{P}_{k}}}\equiv 0\Rightarrow {{Q}_{k}}={{\beta }_{k}}=const \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\dot {P}}_{k}}=-{\frac {\partial H}{\partial {{Q}_{k}}}}\equiv 0\Rightarrow {{P}_{k}}={{\alpha }_{k}}=cons\\&{{\dot {Q}}_{k}}={\frac {\partial {\bar {H}}}{\partial {{P}_{k}}}}\equiv 0\Rightarrow {{Q}_{k}}={{\beta }_{k}}=const\\\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><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><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>H</mi></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><mn>0</mn><mo>⇒</mo><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo>=</mo><msub><mi>α</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo>=</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd></mtr><mtr><mtd></mtd><mtd><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><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>¯</mo></mover></mrow></mrow></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><mo>≡</mo><mn>0</mn><mo>⇒</mo><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo>=</mo><msub><mi>β</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo>=</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi>t</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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