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Display information for equation id:math.1989.8 on revision:1989
* Page found: Hamilton-Jacobische Differenzialgleichung (eq math.1989.8)
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Hash: 657891dc7c1be1ad29c72a6e2a799eb6
TeX (original user input):
\begin{align}
& H(\bar{q},\bar{p},t) \\
& {{p}_{k}}=\frac{\partial S}{\partial {{q}_{k}}} \\
& H(\bar{q},\frac{\partial S}{\partial \bar{q}},t)+\frac{\partial S}{\partial t}=0\quad Ham.Jac.DGL \\
\end{align}
TeX (checked):
{\begin{aligned}&H({\bar {q}},{\bar {p}},t)\\&{{p}_{k}}={\frac {\partial S}{\partial {{q}_{k}}}}\\&H({\bar {q}},{\frac {\partial S}{\partial {\bar {q}}}},t)+{\frac {\partial S}{\partial t}}=0\quad Ham.Jac.DGL\\\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"><mi>H</mi><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><mover><mi>p</mi><mo>¯</mo></mover><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mi>p</mi><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><mi>S</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></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>H</mi><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo>,</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>S</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mover><mi>q</mi><mo>¯</mo></mover></mrow></mrow></mfrac></mrow><mo>,</mo><mi>t</mi><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>S</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mn>0</mn><mspace width="1em"></mspace><mi>H</mi><mi>a</mi><mi>m</mi><mo stretchy="false">.</mo><mi>J</mi><mi>a</mi><mi>c</mi><mo stretchy="false">.</mo><mi>D</mi><mi>G</mi><mi>L</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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