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Display information for equation id:math.1410.210 on revision:1410
* Page found: Symmetrien und Erhaltungsgrößen (eq math.1410.210)
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TeX (original user input):
\begin{align}
& \phi (r)=\arccos \frac{1}{\sqrt{D}}\left( \frac{1}{{{r}^{{}}}}-\frac{mk}{{{l}^{2}}} \right) \\
& \Rightarrow \frac{1}{r(\phi )}=\frac{mk}{{{l}^{2}}}+\sqrt{D}\cos \phi =\frac{mk}{{{l}^{2}}}\left( 1+\varepsilon \cos \phi \right) \\
& mit\quad \varepsilon :=\sqrt{D}\frac{{{l}^{2}}}{mk}=\sqrt{1+\frac{2E{{l}^{2}}}{m{{k}^{2}}}} \\
\end{align}
TeX (checked):
{\begin{aligned}&\phi (r)=\arccos {\frac {1}{\sqrt {D}}}\left({\frac {1}{{r}^{}}}-{\frac {mk}{{l}^{2}}}\right)\\&\Rightarrow {\frac {1}{r(\phi )}}={\frac {mk}{{l}^{2}}}+{\sqrt {D}}\cos \phi ={\frac {mk}{{l}^{2}}}\left(1+\varepsilon \cos \phi \right)\\&mit\quad \varepsilon :={\sqrt {D}}{\frac {{l}^{2}}{mk}}={\sqrt {1+{\frac {2E{{l}^{2}}}{m{{k}^{2}}}}}}\\\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><mi>ϕ</mi><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo><mo>=</mo><mi>arccos</mi><mo>⁡</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mi>D</mi></msqrt></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mi>r</mi><mrow data-mjx-texclass="ORD"></mrow></msup></mrow></mfrac></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><mi>k</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><mi>l</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>r</mi><mo stretchy="false">(</mo><mi>ϕ</mi><mo stretchy="false">)</mo></mrow></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><mi>k</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><mi>l</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><msqrt><mi>D</mi></msqrt></mrow><mi>cos</mi><mo>⁡</mo><mi>ϕ</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><mi>k</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><mi>l</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>1</mn><mo>+</mo><mi>ε</mi><mi>cos</mi><mo>⁡</mo><mi>ϕ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>m</mi><mi>i</mi><mi>t</mi><mspace width="1em"></mspace><mi>ε</mi><mi>:</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><msqrt><mi>D</mi></msqrt></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>l</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><mi>k</mi></mrow></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mn>1</mn><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>E</mi><msup><mi>l</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><msup><mi>k</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow></mrow></msqrt></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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