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Display information for equation id:math.1410.204 on revision:1410

* Page found: Symmetrien und Erhaltungsgrößen (eq math.1410.204)

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TeX (original user input):

\begin{align}
  & \cos \vartheta \acute{\ }:=\frac{1}{\sqrt{D}}\left( \frac{1}{r{{\acute{\ }}^{{}}}}-\frac{mk}{{{l}^{2}}} \right)\Rightarrow \frac{d\cos \vartheta }{dr\acute{\ }}=-\frac{1}{\sqrt{D}}\left( \frac{1}{r{{\acute{\ }}^{2}}} \right) \\ 
 & \frac{d\cos \vartheta }{d\vartheta }=-\sin \vartheta \acute{\ }\Rightarrow -\sin \vartheta d\vartheta =d\cos \vartheta  \\ 
 & -\sin \vartheta \acute{\ }d\vartheta =-\frac{1}{\sqrt{D}}\left( \frac{dr\acute{\ }}{r{{\acute{\ }}^{2}}} \right) \\ 
\end{align}

TeX (checked):

{\begin{aligned}&\cos \vartheta {\acute {\ }}:={\frac {1}{\sqrt {D}}}\left({\frac {1}{r{{\acute {\ }}^{}}}}-{\frac {mk}{{l}^{2}}}\right)\Rightarrow {\frac {d\cos \vartheta }{dr{\acute {\ }}}}=-{\frac {1}{\sqrt {D}}}\left({\frac {1}{r{{\acute {\ }}^{2}}}}\right)\\&{\frac {d\cos \vartheta }{d\vartheta }}=-\sin \vartheta {\acute {\ }}\Rightarrow -\sin \vartheta d\vartheta =d\cos \vartheta \\&-\sin \vartheta {\acute {\ }}d\vartheta =-{\frac {1}{\sqrt {D}}}\left({\frac {dr{\acute {\ }}}{r{{\acute {\ }}^{2}}}}\right)\\\end{aligned}}

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\begin{aligned} \cos ϑ \overset{´}{} : = \frac{1}{\sqrt{D}} (\frac{1}{r {\overset{´}{}}^{}} - \frac{m k}{l^{2}}) \Rightarrow \frac{d \cos ϑ}{d r \overset{´}{}} = - \frac{1}{\sqrt{D}} (\frac{1}{r {\overset{´}{}}^{2}}) \\ \frac{d \cos ϑ}{d ϑ} = - \sin ϑ \overset{´}{} \Rightarrow - \sin ϑ d ϑ = d \cos ϑ \\ - \sin ϑ \overset{´}{} d ϑ = - \frac{1}{\sqrt{D}} (\frac{d r \overset{´}{}}{r {\overset{´}{}}^{2}}) \end{aligned}

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Identifiers

$ϑ$

$\overset{´}{}$

$D$

$r$

$\overset{´}{}$

$m$

$k$

$l$

$d$

$ϑ$

$d$

$r$

$\overset{´}{}$

$D$

$r$

$\overset{´}{}$

$d$

$ϑ$

$d$

$ϑ$

$ϑ$

$\overset{´}{}$

$ϑ$

$d$

$ϑ$

$d$

$ϑ$

$ϑ$

$\overset{´}{}$

$d$

$ϑ$

$D$

$d$

$r$

$\overset{´}{}$

$r$

$\overset{´}{}$

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