Merge branch 'master' of https://github.com/AndreasFMueller/SeminarSpezielleFunktionen

7 files changed, 101 insertions, 4 deletions

diff --git a/buch/papers/lambertw/Bilder/Abstand.py b/buch/papers/lambertw/Bilder/Abstand.py
new file mode 100644
index 0000000..d787c34
--- /dev/null
+++ b/buch/papers/lambertw/Bilder/Abstand.py
@@ -0,0 +1,18 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Sat Jul 30 23:09:33 2022
+
+@author: yanik
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+phi = np.pi/2
+t = np.linspace(0, 10, 10**5)
+x0 = 1
+
+def D(t):
+    return np.sqrt(x0**2+2*x0*t*np.cos(phi)+2*t**2-2*t**2*np.sin(phi))
+
+plt.plot(t, D(t))
diff --git a/buch/papers/lambertw/Bilder/Intuition.pdf b/buch/papers/lambertw/Bilder/Intuition.pdf
new file mode 100644
index 0000000..739b02b
--- /dev/null
+++ b/buch/papers/lambertw/Bilder/Intuition.pdf
diff --git a/buch/papers/lambertw/Bilder/Strategie.pdf b/buch/papers/lambertw/Bilder/Strategie.pdf
index 0de3001..b5428f5 100644
--- a/buch/papers/lambertw/Bilder/Strategie.pdf
+++ b/buch/papers/lambertw/Bilder/Strategie.pdf
diff --git a/buch/papers/lambertw/Bilder/Strategie.py b/buch/papers/lambertw/Bilder/Strategie.py
index b9b41bf..975e248 100644
--- a/buch/papers/lambertw/Bilder/Strategie.py
+++ b/buch/papers/lambertw/Bilder/Strategie.py
@@ -34,7 +34,8 @@ ax.quiver(X, Y, U, W, angles='xy', scale_units='xy', scale=1, headwidth=5, headl
 
 ax.plot([V[0], (VZ+V)[0]], [V[1], (VZ+V)[1]], 'k--')
 ax.plot(np.vstack([V, Z])[:, 0], np.vstack([V, Z])[:,1], 'bo', markersize=10)
-
+ax.set_xlabel("x", size=20)
+ax.set_ylabel("y", size=20)
 
 ax.text(2.5, 4.5, "Visierlinie", size=20, rotation=10)
 
@@ -44,9 +45,9 @@ plt.rcParams.update({
     "font.serif": ["New Century Schoolbook"],
 })
 
-ax.text(1.6, 4.3, r"$\vec{v}$", size=30)
-ax.text(0.6, 3.9, r"$V$", size=30, c='b')
-ax.text(5.1, 4.77, r"$Z$", size=30, c='b')
+ax.text(1.6, 4.3, r"$\dot{v}$", size=20)
+ax.text(0.65, 3.9, r"$V$", size=20, c='b')
+ax.text(5.15, 4.85, r"$Z$", size=20, c='b')
 
 
 
diff --git a/buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png b/buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png
index 90758cd..e6e7c1e 100644
--- a/buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png
+++ b/buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png
diff --git a/buch/papers/lambertw/Bilder/konvergenz.py b/buch/papers/lambertw/Bilder/konvergenz.py
new file mode 100644
index 0000000..dac99a7
--- /dev/null
+++ b/buch/papers/lambertw/Bilder/konvergenz.py
@@ -0,0 +1,20 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Sun Jul 31 14:34:13 2022
+
+@author: yanik
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+t = 0
+phi = np.linspace(np.pi/2, 3*np.pi/2, 10**5)
+x0 = 1
+y0 = -2
+
+def D(t):
+    return (x0+t*np.cos(phi))*np.cos(phi)+(y0+t*(np.sin(phi)-1))*(np.sin(phi)-1)/(np.sqrt((x0+t*np.cos(phi))**2+(y0+t*(np.sin(phi)-1))**2))
+
+
+plt.plot(phi, D(t))
\ No newline at end of file
diff --git a/buch/papers/lambertw/Bilder/lambertAbstandBauchgefühl.py b/buch/papers/lambertw/Bilder/lambertAbstandBauchgefühl.py
new file mode 100644
index 0000000..3a90afa
--- /dev/null
+++ b/buch/papers/lambertw/Bilder/lambertAbstandBauchgefühl.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-0.08, r"$\dot{v}$", size=20)
+plt.text(xmin-0.02, ymin+0.05, r"$V$", size=20, c='b')
+plt.text(0.02, ymin+0.05, r"$Z$", size=20, c='b')
\ No newline at end of file