From 4da8d15f58b595f9a2fdedb3f7ca2130eac4a3e6 Mon Sep 17 00:00:00 2001
From: hanemile <emile.hansmaennel@gmail.com>
Date: Mon, 4 Dec 2017 22:34:36 +0100
Subject: updated langfassung

---
 langfassung/docs/2_einleitung.tex | 47 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 47 insertions(+)

(limited to 'langfassung/docs/2_einleitung.tex')

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
-- 
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