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author | haddoucher <reda.haddouche@ost.ch> | 2022-08-16 14:36:07 +0200 |
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committer | haddoucher <reda.haddouche@ost.ch> | 2022-08-16 14:36:07 +0200 |
commit | f031b148a79d1dafb0e3405643be05e7a7eb1222 (patch) | |
tree | 3f0c7d27ba90e10874a885cae9026fdbaa0b01e6 /buch/papers/lambertw/Bilder/lambertAbstandBauchgefühl.py | |
parent | Update tschebyscheff_beispiel.tex (diff) | |
parent | Merge pull request #5 from haddoucher/sturmliouville/erik-branch (diff) | |
download | SeminarSpezielleFunktionen-f031b148a79d1dafb0e3405643be05e7a7eb1222.tar.gz SeminarSpezielleFunktionen-f031b148a79d1dafb0e3405643be05e7a7eb1222.zip |
Merge remote-tracking branch 'origin/master' into sturmliouville/redabranch
Diffstat (limited to 'buch/papers/lambertw/Bilder/lambertAbstandBauchgefühl.py')
-rw-r--r-- | buch/papers/lambertw/Bilder/lambertAbstandBauchgefühl.py | 58 |
1 files changed, 58 insertions, 0 deletions
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')
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