Zur Navigation springen
Zur Suche springen
General
Display information for equation id:math.1325.162 on revision:1325
* Page found: Der Hamiltonsche kanonische Formalismus (eq math.1325.162)
(force rerendering)Occurrences on the following pages:
Hash: 5f4a2dd0c01173e2e423d1d93c0963d1
TeX (original user input):
\begin{align}
& J{{\left( J{{M}^{-1}} \right)}^{T}}=\left( \begin{matrix}
0 & 1 \\
-1 & 0 \\
\end{matrix} \right){{\left[ \left( \begin{matrix}
0 & 1 \\
-1 & 0 \\
\end{matrix} \right)\left( \begin{matrix}
\frac{\partial Q}{\partial q} & \frac{\partial Q}{\partial p} \\
\frac{\partial P}{\partial q} & \frac{\partial P}{\partial p} \\
\end{matrix} \right) \right]}^{T}}=\left( \begin{matrix}
0 & 1 \\
-1 & 0 \\
\end{matrix} \right){{\left( \begin{matrix}
\frac{\partial P}{\partial q} & \frac{\partial P}{\partial p} \\
-\frac{\partial Q}{\partial q} & -\frac{\partial Q}{\partial p} \\
\end{matrix} \right)}^{T}} \\
& =\left( \begin{matrix}
0 & 1 \\
-1 & 0 \\
\end{matrix} \right){{\left( \begin{matrix}
{{\left( \frac{\partial P}{\partial q} \right)}^{T}} & -{{\left( \frac{\partial Q}{\partial q} \right)}^{T}} \\
{{\left( \frac{\partial P}{\partial p} \right)}^{T}} & -{{\left( \frac{\partial Q}{\partial p} \right)}^{T}} \\
\end{matrix} \right)}^{{}}}=\left( \begin{matrix}
{{\left( \frac{\partial P}{\partial p} \right)}^{T}} & -{{\left( \frac{\partial Q}{\partial p} \right)}^{T}} \\
-{{\left( \frac{\partial P}{\partial q} \right)}^{T}} & {{\left( \frac{\partial Q}{\partial q} \right)}^{T}} \\
\end{matrix} \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&J{{\left(J{{M}^{-1}}\right)}^{T}}=\left({\begin{matrix}0&1\\-1&0\\\end{matrix}}\right){{\left[\left({\begin{matrix}0&1\\-1&0\\\end{matrix}}\right)\left({\begin{matrix}{\frac {\partial Q}{\partial q}}&{\frac {\partial Q}{\partial p}}\\{\frac {\partial P}{\partial q}}&{\frac {\partial P}{\partial p}}\\\end{matrix}}\right)\right]}^{T}}=\left({\begin{matrix}0&1\\-1&0\\\end{matrix}}\right){{\left({\begin{matrix}{\frac {\partial P}{\partial q}}&{\frac {\partial P}{\partial p}}\\-{\frac {\partial Q}{\partial q}}&-{\frac {\partial Q}{\partial p}}\\\end{matrix}}\right)}^{T}}\\&=\left({\begin{matrix}0&1\\-1&0\\\end{matrix}}\right){{\left({\begin{matrix}{{\left({\frac {\partial P}{\partial q}}\right)}^{T}}&-{{\left({\frac {\partial Q}{\partial q}}\right)}^{T}}\\{{\left({\frac {\partial P}{\partial p}}\right)}^{T}}&-{{\left({\frac {\partial Q}{\partial p}}\right)}^{T}}\\\end{matrix}}\right)}^{}}=\left({\begin{matrix}{{\left({\frac {\partial P}{\partial p}}\right)}^{T}}&-{{\left({\frac {\partial Q}{\partial p}}\right)}^{T}}\\-{{\left({\frac {\partial P}{\partial q}}\right)}^{T}}&{{\left({\frac {\partial Q}{\partial q}}\right)}^{T}}\\\end{matrix}}\right)\\\end{aligned}}
LaTeXML (experimentell; verwendet MathML) rendering
MathML (0 B / 8 B) :
SVG image empty. Force Re-Rendering
SVG (0 B / 8 B) :
MathML (experimentell; keine Bilder) rendering
MathML (8.975 KB / 551 B) :
<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><mi>J</mi><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>J</mi><msup><mi>M</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>1</mn></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><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><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</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><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>Q</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>q</mi></mrow></mrow></mfrac></mrow></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>Q</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>p</mi></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>P</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>q</mi></mrow></mrow></mfrac></mrow></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>P</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>p</mi></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><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><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>P</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>q</mi></mrow></mrow></mfrac></mrow></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>P</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>p</mi></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>Q</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>q</mi></mrow></mrow></mfrac></mrow></mtd><mtd><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>Q</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>p</mi></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><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><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>P</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>q</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup></mtd><mtd><mo>−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>Q</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>q</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup></mtd></mtr><mtr><mtd><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>P</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>p</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup></mtd><mtd><mo>−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>Q</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>p</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"></mrow></msup><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><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>P</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>p</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup></mtd><mtd><mo>−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>Q</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>p</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup></mtd></mtr><mtr><mtd><mo>−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>P</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>q</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup></mtd><mtd><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>Q</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>q</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup></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>
Translations to Computer Algebra Systems
Translation to Maple
In Maple:
Translation to Mathematica
In Mathematica:
Similar pages
Calculated based on the variables occurring on the entire Der Hamiltonsche kanonische Formalismus page
Identifiers
MathML observations
0results
0results
no statistics present please run the maintenance script ExtractFeatures.php
0 results
0 results