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Display information for equation id:math.1970.3 on revision:1970
* Page found: Der Satz von Liouville (eq math.1970.3)
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Hash: 566200e42bfb4264ecd8d010e0985c0f
TeX (original user input):
\begin{align}
& \left( q,p \right)\in \Gamma \\
& \dot{q}=p \\
& \dot{p}=-{{\omega }_{0}}^{2}q \\
& \dot{\bar{x}}=A\bar{x} \\
& A=\left( \begin{matrix}
0 & 1 \\
-{{\omega }_{0}}^{2} & 0 \\
\end{matrix} \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&\left(q,p\right)\in \Gamma \\&{\dot {q}}=p\\&{\dot {p}}=-{{\omega }_{0}}^{2}q\\&{\dot {\bar {x}}}=A{\bar {x}}\\&A=\left({\begin{matrix}0&1\\-{{\omega }_{0}}^{2}&0\\\end{matrix}}\right)\\\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><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>q</mi><mo>,</mo><mi>p</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>∈</mo><mi mathvariant="normal">Γ</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>q</mi><mo>˙</mo></mover></mrow></mrow><mo>=</mo><mi>p</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>˙</mo></mover></mrow></mrow><mo>=</mo><mo>−</mo><msup><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>q</mi></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>¯</mo></mover></mrow></mrow><mo>˙</mo></mover></mrow></mrow><mo>=</mo><mi>A</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>x</mi><mo>¯</mo></mover></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>A</mi><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mo>−</mo><msup><msub><mi>ω</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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