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op
Einleitung
\subsection{Themen}
\begin{itemize}
\item Heidelberg bla
\item Galaxy Foo bla
\item Stauchen / Strecken bla
\item Problem: Geschwindigkeit bla
\item Benchmarks:
\begin{itemize}
\item 10000 Sterne - 1 Stern
\item ...
\end{itemize}
\end{itemize}
\subsection{Motivation}
\paragraph{ \( \Phi \) }
\begin{equation}
\Phi(r) = - \frac{4\pi G \rho_0 R_s^3}{r} \ln ( 1+ \frac{r}{R_s} )
\end{equation}
with the limits
\begin{equation}
\lim_{r\to \infty} \Phi=0
\end{equation}
and
\begin{equation}
\lim_{r\to 0} \Phi=-4\pi G\rho_0 R_s^2
\end{equation}
\paragraph{ \( \rho \) }
\begin{equation}
\rho(r) = \frac{1}{\sqrt{2 \cdot \pi} \cdot \sigma} \cdot
e^{\left( - \frac{(\Phi(r)}{\sigma^{2}} \right)}
\end{equation}
\paragraph{\( \rho_{new} \rightarrow (deriviation) \) }
\begin{equation}
\rho(r) \cdot 1-\frac{1}{(2 \cdot sigma^{2} )} \cdot
( Mxx \cdot x^{2} + 2 \cdot Mxy \cdot xy + Myy \cdot y^{2} ))
\end{equation}
% def rho_new(x, y, z):
% a = (1 - ((1) / (2 * (sigma ** 2))) * ( Mxx * x**2 + 2 * Mxy * x * y + Myy * y**2 ) )
% return rho(x, y, z) * a
%
% # phi function
% def phi(x):
% if x == 0:
% return -4 * pi * f_0 * G * R_s**2
%
% a = - ( 4 * pi * G * f_0 * R_s ** 3 ) / x
% b = np.log(1. + (x / R_s) )
% c = a * b
% return c
Motivations blah
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