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Display information for equation id:math.1130.15 on revision:1130
* Page found: Effektives Potential (eq math.1130.15)
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Hash: 452dcc530b9e9f430707b93fca72bd0b
TeX (original user input):
\begin{align}
& \Rightarrow \frac{1}{2}\mu {{\left( \frac{dr}{dt} \right)}^{2}}=E-U \\
& \Leftrightarrow {{\left( \frac{dr}{dt} \right)}^{2}}=\frac{2}{\mu }\left( E-U \right) \\
& \Leftrightarrow dt=\frac{dr}{\sqrt{\frac{2}{\mu }\left( E-U \right)}} \\
\end{align}
TeX (checked):
{\begin{aligned}&\Rightarrow {\frac {1}{2}}\mu {{\left({\frac {dr}{dt}}\right)}^{2}}=E-U\\&\Leftrightarrow {{\left({\frac {dr}{dt}}\right)}^{2}}={\frac {2}{\mu }}\left(E-U\right)\\&\Leftrightarrow dt={\frac {dr}{\sqrt {{\frac {2}{\mu }}\left(E-U\right)}}}\\\end{aligned}}
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MathML (experimentell; keine Bilder) rendering
MathML (2.457 KB / 417 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><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>μ</mi><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>d</mi><mi>r</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mi>E</mi><mo>−</mo><mi>U</mi></mtd></mtr><mtr><mtd></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>d</mi><mi>r</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></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>2</mn></mrow><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>E</mi><mo>−</mo><mi>U</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇔</mo><mi>d</mi><mi>t</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>r</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>E</mi><mo>−</mo><mi>U</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></msqrt></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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