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Display information for equation id:math.1411.141 on revision:1411
* Page found: Symmetrien und Erhaltungsgrößen (eq math.1411.141)
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Hash: be3d288a7e45d8b312c877d0c9c16474
TeX (original user input):
\begin{align}
& {{{\bar{r}}}_{1}}=\bar{R}+\frac{{{m}_{2}}}{M}{{{\bar{r}}}_{{}}}\quad \quad {{{\bar{r}}}_{2}}=\bar{R}-\frac{{{m}_{1}}}{M}\bar{r} \\
& {{{\dot{\bar{r}}}}_{1}}=\dot{\bar{R}}+\frac{{{m}_{2}}}{M}{{{\dot{\bar{r}}}}_{{}}}\quad \quad {{{\dot{\bar{r}}}}_{2}}=\dot{\bar{R}}-\frac{{{m}_{1}}}{M}{{{\dot{\bar{r}}}}_{{}}} \\
& L=\frac{M}{2}{{{\dot{\bar{R}}}}^{2}}+\frac{1}{2}m{{{\dot{\bar{r}}}}^{2}}-V(r) \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\bar {r}}_{1}}={\bar {R}}+{\frac {{m}_{2}}{M}}{{\bar {r}}_{}}\quad \quad {{\bar {r}}_{2}}={\bar {R}}-{\frac {{m}_{1}}{M}}{\bar {r}}\\&{{\dot {\bar {r}}}_{1}}={\dot {\bar {R}}}+{\frac {{m}_{2}}{M}}{{\dot {\bar {r}}}_{}}\quad \quad {{\dot {\bar {r}}}_{2}}={\dot {\bar {R}}}-{\frac {{m}_{1}}{M}}{{\dot {\bar {r}}}_{}}\\&L={\frac {M}{2}}{{\dot {\bar {R}}}^{2}}+{\frac {1}{2}}m{{\dot {\bar {r}}}^{2}}-V(r)\\\end{aligned}}
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MathML (4.717 KB / 491 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><msub><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>1</mn></mrow></msub><mo>=</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>R</mi><mo>¯</mo></mover></mrow></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mi>M</mi></mrow></mfrac></mrow><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></msub><mspace width="1em"></mspace><mspace width="1em"></mspace><msub><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></msub><mo>=</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>R</mi><mo>¯</mo></mover></mrow></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mi>M</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>=</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>R</mi><mo>¯</mo></mover></mrow></mrow><mo>˙</mo></mover></mrow></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mi>M</mi></mrow></mfrac></mrow><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></msub><mspace width="1em"></mspace><mspace width="1em"></mspace><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>=</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>R</mi><mo>¯</mo></mover></mrow></mrow><mo>˙</mo></mover></mrow></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mi>M</mi></mrow></mfrac></mrow><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><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><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>R</mi><mo>¯</mo></mover></mrow></mrow><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mi>m</mi><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>˙</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><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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