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diff --git a/langfassung/docs/2_einleitung.tex b/langfassung/docs/2_einleitung.tex index 806c214..bce9ec8 100644 --- a/langfassung/docs/2_einleitung.tex +++ b/langfassung/docs/2_einleitung.tex @@ -1,3 +1,4 @@ +op Einleitung \subsection{Themen} @@ -16,4 +17,50 @@ Einleitung \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 |
