159:= invmatrix @ np.array(, ]) rs = np.sqrt(r2z2) zs = np.sqrt(r2z2) return rs * np.cos(thetas), rs * np.sin(thetas), zs if E2 < E and E < E1: xs = np.zeros(orbit_res) rs = np.zeros(orbit_res) for i, theta in enumerate(thetas): invmatrix = scipy.linalg.inv(np.array(, ])) x2r2 = invmatrix @ np.array(, ]) xs = np.sqrt(x2r2) rs = np.sqrt(x2r2) return xs, rs * np.cos(thetas), rs * np.sin(thetas)
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thetas = np.linspace(0, 2*np.pi, orbit_res) if E3 < E and E < E2: rs = np.zeros(orbit_res) zs = np.zeros(orbit_res) for i, theta in enumerate(thetas): invmatrix = scipy.linalg.inv(np.array(, ])) r2z2
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Given fixed angular momentum, for each value of kinetic energy, we have a family of curves for the possible value of angular velocity. The curves are plotted in black, on the orange ellipsoid of fixed angular momentum.
290:– You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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u = np.linspace(0, 2 * np.pi, 100) v = np.linspace(0, np.pi, 100) x = np.outer(np.cos(u), np.sin(v)) y = np.outer(np.sin(u), np.sin(v)) z = np.outer(np.ones(np.size(u)), np.cos(v)) x *= L/I1 y *= L/I2 z *= L/I3
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xs, ys, zs = parametric_plot(E) xs *= 1+epsilon ys *= 1+epsilon zs *= 1+epsilon ax.plot3D(xs, ys, zs, linewidth=1, color='k') ax.plot3D(-xs, -ys, -zs, linewidth=1, color='k')
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L = 1.0 L2 = L**2 I1, I2, I3 = 1.0, 2.0, 3.0 xmin, xmax, ymin, ymax, zmin, zmax = -L/I1, L/I1, -L/I2, L/I2, -L/I3, L/I3 E1, E2, E3 = 0.5*L2/I1, 0.5*L2/I2, 0.5*L2/I3
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This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
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If the file has been modified from its original state, some details may not fully reflect the modified file.
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The following pages on the
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ax.axes.set_xlim3d(xmin, xmax) ax.axes.set_ylim3d(ymin, ymax) ax.axes.set_zlim3d(zmin, zmax)
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I, the copyright holder of this work, hereby publish it under the following license:
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Uploaded while editing "Tennis racket theorem" on en.wikipedia.org
144:```python import numpy as np import matplotlib.pyplot as plt import scipy
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fig = plt.figure(figsize = (16,16)) ax = plt.axes(projection='3d')
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epsilon=1e-3 for E in np.linspace(E3+epsilon, E1-epsilon, 20):
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Creative
Commons Attribution-ShareAlike 4.0 International
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Add a one-line explanation of what this file represents
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Contour plot of all solutions to Euler's equations.png
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ax.plot_surface(x, y, z, color='orange', alpha=0.3)
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Commons is a freely licensed media file repository.
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260:Attribution-Share Alike 4.0 International
181:ax.set_aspect('equal') ax.set_axis_off()
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186:```
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
