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Display information for equation id:math.1957.24 on revision:1957
* Page found: Kanonische Transformationen (eq math.1957.24)
(force rerendering)Occurrences on the following pages:
Hash: efdda20cd207cca7247a7fa9b26513b6
TeX (original user input):
\begin{align}
& H={{p}_{r}}\dot{r}+{{p}_{\phi }}\dot{\phi }-L=m{{{\dot{r}}}^{2}}+m{{r}^{2}}{{{\dot{\phi }}}^{2}}-L=\frac{m}{2}\left( {{{\dot{r}}}^{2}}+{{r}^{2}}{{{\dot{\phi }}}^{2}} \right)+V(r) \\
& H=\frac{{{p}_{r}}^{2}}{2m}+\frac{{{p}_{\phi }}^{2}}{2m{{r}^{2}}}+V(r) \\
\end{align}
TeX (checked):
{\begin{aligned}&H={{p}_{r}}{\dot {r}}+{{p}_{\phi }}{\dot {\phi }}-L=m{{\dot {r}}^{2}}+m{{r}^{2}}{{\dot {\phi }}^{2}}-L={\frac {m}{2}}\left({{\dot {r}}^{2}}+{{r}^{2}}{{\dot {\phi }}^{2}}\right)+V(r)\\&H={\frac {{{p}_{r}}^{2}}{2m}}+{\frac {{{p}_{\phi }}^{2}}{2m{{r}^{2}}}}+V(r)\\\end{aligned}}
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MathML (2.929 KB / 477 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>H</mi><mo>=</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>˙</mo></mover></mrow></mrow><mo>+</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>ϕ</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ϕ</mi><mo>˙</mo></mover></mrow></mrow><mo>−</mo><mi>L</mi><mo>=</mo><mi>m</mi><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>m</mi><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ϕ</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><mi>L</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ϕ</mi><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>+</mo><mi>V</mi><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi>H</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi></mrow></mrow></mfrac></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>ϕ</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mo>+</mo><mi>V</mi><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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