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Display information for equation id:math.1981.7 on revision:1981
* Page found: Hamilton-Jacobische Differenzialgleichung (eq math.1981.7)
(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 xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mover><mi>P</mi><mo>˙</mo></mover><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">=</mo><mo stretchy="false">−</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 stretchy="false">≡</mo><mn>0</mn><mo stretchy="false">⇒</mo><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">=</mo><msub><mi>α</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">=</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi>s</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mover><mi>Q</mi><mo>˙</mo></mover><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mover><mi>H</mi><mo>¯</mo></mover></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 stretchy="false">≡</mo><mn>0</mn><mo stretchy="false">⇒</mo><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">=</mo><msub><mi>β</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">=</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi>t</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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