– PhysikWiki

General

Display information for equation id:math.1995.34 on revision:1995

* Page found: Wirkungs- und Winkelvariable (eq math.1995.34)

Occurrences on the following pages:

Wirkungs- und Winkelvariable Eq: math.1995.34

Hash: 0f78b956640a1a8a9e0ff2a154ae0abe

TeX (original user input):

\begin{align}
  & I(E)=\oint{pdq}=2m\omega \int\limits_{{{q}_{-}}}^{{{q}_{+}}}{{}}\sqrt{\frac{2E}{m{{\omega }^{2}}}-{{q}^{2}}}dq \\
 & I(E)=2m\omega \left[ \frac{q}{2}\sqrt{\frac{2E}{m{{\omega }^{2}}}-{{q}^{2}}}+\frac{E}{m{{\omega }^{2}}}\arcsin \frac{q}{\sqrt{\frac{2E}{m{{\omega }^{2}}}}} \right]_{q+}^{q-}=\frac{2\pi }{\omega }E \\
\end{align}

TeX (checked):

{\begin{aligned}&I(E)=\oint {pdq}=2m\omega \int \limits _{{q}_{-}}^{{q}_{+}}{}{\sqrt {{\frac {2E}{m{{\omega }^{2}}}}-{{q}^{2}}}}dq\\&I(E)=2m\omega \left[{\frac {q}{2}}{\sqrt {{\frac {2E}{m{{\omega }^{2}}}}-{{q}^{2}}}}+{\frac {E}{m{{\omega }^{2}}}}\arcsin {\frac {q}{\sqrt {\frac {2E}{m{{\omega }^{2}}}}}}\right]_{q+}^{q-}={\frac {2\pi }{\omega }}E\\\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 (3.549 KB / 578 B) :

\begin{aligned} I (E) = \oint p d q = 2 m ω \int_{q_{-}}^{q_{+}} \sqrt{\frac{2 E}{m ω^{2}} - q^{2}} d q \\ I (E) = 2 m ω {[\frac{q}{2} \sqrt{\frac{2 E}{m ω^{2}} - q^{2}} + \frac{E}{m ω^{2}} \arcsin \frac{q}{\sqrt{\frac{2 E}{m ω^{2}}}}]}_{q +}^{q -} = \frac{2 π}{ω} E \end{aligned}

<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>I</mi><mo stretchy="false">(</mo><mi>E</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true"><mo>&#x222E;</mo></mstyle><mrow data-mjx-texclass="ORD"><mi>p</mi><mi>d</mi><mi>q</mi></mrow><mo>=</mo><mn>2</mn><mi>m</mi><mi>&#x03C9;</mi><munderover><mo form="prefix" texclass="OP">&#x222B;</mo><mrow data-mjx-texclass="ORD"><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msub></mrow></munderover><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>E</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><msup><mi>&#x03C9;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mo>&#x2212;</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></msqrt></mrow><mi>d</mi><mi>q</mi></mtd></mtr><mtr><mtd></mtd><mtd><mi>I</mi><mo stretchy="false">(</mo><mi>E</mi><mo stretchy="false">)</mo><mo>=</mo><mn>2</mn><mi>m</mi><mi>&#x03C9;</mi><msubsup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>E</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><msup><mi>&#x03C9;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mo>&#x2212;</mo><msup><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></msqrt></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>E</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><msup><mi>&#x03C9;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mi>arcsin</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>q</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>E</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><msup><mi>&#x03C9;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow></msqrt></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>q</mi><mo>+</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>q</mi><mo>&#x2212;</mo></mrow></mrow></msubsup><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>&#x03C0;</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>&#x03C9;</mi></mrow></mfrac></mrow><mi>E</mi></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:

Identifiers

$I$

$E$

$p$

$d$

$q$

$m$

$ω$

$q_{-}$

$q_{+}$

$E$

$m$

$ω$

$q$

$q$

$I$

$E$

$m$

$ω$

$q$

$E$

$m$

$ω$

$q$

$E$

$m$

$ω$

$q$

$E$

$m$

$ω$

$q$

$q$

$π$

$ω$

$E$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimentell; verwendet MathML) rendering

MathML (experimentell; keine Bilder) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigationsmenü

General

LaTeXML (experimentell; verwendet MathML) rendering

MathML (experimentell; keine Bilder) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigationsmenü

Suche