From 8dc531ac53ae1b085482c9f1bda6001ca803c164 Mon Sep 17 00:00:00 2001
From: Kuster Yanik <yanik.kuster@ost.ch>
Date: Tue, 2 Aug 2022 21:14:53 +0200
Subject: Created python files for graphics. Created addtional subsection
 verlockende Intuition

---
 .../Bilder/lambertAbstandBauchgef\303\274hl.py"    | 58 ++++++++++++++++++++++
 1 file changed, 58 insertions(+)
 create mode 100644 "buch/papers/lambertw/Bilder/lambertAbstandBauchgef\303\274hl.py"

(limited to 'buch/papers/lambertw/Bilder/lambertAbstandBauchgefühl.py')

diff --git "a/buch/papers/lambertw/Bilder/lambertAbstandBauchgef\303\274hl.py" "b/buch/papers/lambertw/Bilder/lambertAbstandBauchgef\303\274hl.py"
new file mode 100644
index 0000000..9031bfc
--- /dev/null
+++ "b/buch/papers/lambertw/Bilder/lambertAbstandBauchgef\303\274hl.py"
@@ -0,0 +1,58 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Sun Jul 31 13:32:53 2022
+
+@author: yanik
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+import scipy.special as sci
+
+W = sci.lambertw
+
+
+t = np.linspace(0, 1.2, 1000)
+x0 = 1
+y0 = 1
+
+r0 = np.sqrt(x0**2+y0**2)
+chi = (r0+y0)/(r0-y0)
+
+x = x0*np.sqrt(1/chi*W(chi*np.exp(chi-4*t/(r0-y0))))
+eta = (x/x0)**2
+y = 1/4*((y0+r0)*eta+(y0-r0)*np.log(eta)-r0+3*y0)
+
+ymin= (min(y)).real
+xmin = (x[np.where(y == ymin)][0]).real
+
+
+#Verfolger
+plt.plot(x, y, 'r--')
+plt.plot(xmin, ymin, 'bo', markersize=10)
+
+#Ziel
+plt.plot(np.zeros_like(t), t, 'g--')
+plt.plot(0, ymin, 'bo', markersize=10)
+
+
+plt.plot([0, xmin], [ymin, ymin], 'k--')
+#plt.xlim(-0.1, 1)
+#plt.ylim(1, 2)
+#plt.ylabel("y")
+#plt.xlabel("x")
+plt.grid(True)
+plt.quiver(xmin, ymin, -0.2, 0, scale=1)
+
+plt.text(xmin+0.1, ymin-0.1, "Verfolgungskurve", size=20, rotation=20, color='r')
+plt.text(0.01, 0.02, "Fluchtkurve", size=20, rotation=90, color='g')
+
+plt.rcParams.update({
+    "text.usetex": True,
+    "font.family": "serif",
+    "font.serif": ["New Century Schoolbook"],
+})
+
+plt.text(xmin-0.11, ymin-0.12, r"$\dot{v}$", size=30)
+plt.text(xmin-0.02, ymin+0.05, r"$V$", size=30, c='b')
+plt.text(0.02, ymin+0.05, r"$Z$", size=30, c='b')
\ No newline at end of file
-- 
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