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Display information for equation id:math.1964.5 on revision:1964
* Page found: Symplektische Struktur des Phasenraums (eq math.1964.5)
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Hash: 6bad951ac2f619cf34cb1048c099d0c3
TeX (original user input):
\begin{align}
& \bar{x}:=\left( \begin{matrix}
{{q}_{1}} \\
... \\
{{q}_{f}} \\
{{p}_{1}} \\
... \\
{{p}_{f}} \\
\end{matrix} \right) \\
& {{{\bar{H}}}_{x}}:=\left( \begin{matrix}
\frac{\partial H}{\partial {{q}_{1}}} \\
... \\
\frac{\partial H}{\partial {{q}_{f}}} \\
\frac{\partial H}{\partial {{p}_{1}}} \\
... \\
\frac{\partial H}{\partial {{p}_{f}}} \\
\end{matrix} \right)\quad \quad J:=\left( \begin{matrix}
0 & {{1}_{f}} \\
-{{1}_{f}} & 0 \\
\end{matrix} \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&{\bar {x}}:=\left({\begin{matrix}{{q}_{1}}\\...\\{{q}_{f}}\\{{p}_{1}}\\...\\{{p}_{f}}\\\end{matrix}}\right)\\&{{\bar {H}}_{x}}:=\left({\begin{matrix}{\frac {\partial H}{\partial {{q}_{1}}}}\\...\\{\frac {\partial H}{\partial {{q}_{f}}}}\\{\frac {\partial H}{\partial {{p}_{1}}}}\\...\\{\frac {\partial H}{\partial {{p}_{f}}}}\\\end{matrix}}\right)\quad \quad J:=\left({\begin{matrix}0&{{1}_{f}}\\-{{1}_{f}}&0\\\end{matrix}}\right)\\\end{aligned}}
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MathML (3.573 KB / 506 B) :
<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"><mover><mi>x</mi><mo>¯</mo></mover><mo stretchy="false">:=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN"></mo><mtable><mtr><mtd><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>...</mi></mtd></mtr><mtr><mtd><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>...</mi></mtd></mtr><mtr><mtd><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true" data-mjx-texclass="CLOSE"></mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mover><mi>H</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mi>x</mi></mrow></msub><mo stretchy="false">:=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN"></mo><mtable><mtr><mtd><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"><mn>1</mn></mrow></msub></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mi>...</mi></mtd></mtr><mtr><mtd><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>f</mi></mrow></msub></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><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>p</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mi>...</mi></mtd></mtr><mtr><mtd><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>p</mi><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub></mrow></mrow></mfrac></mrow></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true" data-mjx-texclass="CLOSE"></mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mspace width="1em"></mspace><mspace width="1em"></mspace><mi>J</mi><mo stretchy="false">:=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN"></mo><mtable><mtr><mtd><mn>0</mn></mtd><mtd><msub><mn>1</mn><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub></mtd></mtr><mtr><mtd><mo stretchy="false">−</mo><msub><mn>1</mn><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub></mtd><mtd><mn>0</mn></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true" data-mjx-texclass="CLOSE"></mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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