Fayl:Phase portrait of damped oscillator, with increasing damping strength.gif
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Qisqa izoh
TaʼrifPhase portrait of damped oscillator, with increasing damping strength.gif |
English: ```python
import numpy as np import matplotlib.pyplot as plt from math import isclose from numpy import linalg as LA import matplotlib.cm as cm def plot_circle(v_1, v_2, ax, **kwargs): angles = np.linspace(0, 2*np.pi, 100) points = v_1[:,np.newaxis] * np.cos(angles) + v_2[:,np.newaxis] * np.sin(angles) ax.plot(points[0,:], points[1,:], **kwargs) def plot_vector_field(A, xmin=-5, xmax=5, ymin=-5, ymax=5, title=""): axx, axy = A[0,0], A[0,1] ayx, ayy = A[1,0], A[1,1] det = axx * ayy - axy * ayx tr = axx + ayy eigen_vals, eigen_vects = LA.eig(A) is_critical = abs(eigen_vals[0] - eigen_vals[1]) / abs(eigen_vals[0]) < 1e-2 delta = tr**2 - 4*det is_rotational = delta <= 0 and not is_critical # Initialize plotting object fig, axes = plt.subplot_mosaic("133;233", figsize=(18,12)) colormap=cm.viridis # pole-zero plot ax = axes['1'] ax.scatter(eigen_vals[0].real, eigen_vals[0].imag, color=colormap(eigen_vals[0].real)) ax.scatter(eigen_vals[1].real, eigen_vals[1].imag, color=colormap(eigen_vals[1].real)) r = np.sqrt(abs(eigen_vals[0] * eigen_vals[1])) plot_circle(np.array([r, 0]), np.array([0, r]), ax, color='k', alpha=0.3) ax.plot([xmin, xmax], np.zeros(2), color='k', alpha=0.2) ax.plot(np.zeros(2), [ymin, ymax], color='k', alpha=0.2) ax.set_aspect('equal') ax.set_xlim([-2, 2]) ax.set_ylim([-2, 2]) ax.set_xlabel('Real') ax.set_ylabel('Imag') ax.set_title('pole-zero plot') # stability plot ax = axes['2'] xs = np.linspace(xmin, xmax, 100) ys = xs**2 / 4 ax.plot(xs, ys) ax.scatter(tr, det, color='red') ax.plot([xmin, xmax], np.zeros(2), color='k', alpha=0.2) ax.plot(np.zeros(2), [ymin, ymax], color='k', alpha=0.2) ax.set_aspect('equal') ax.set_xlim([-4,2]) ax.set_ylim([-1, 5]) ax.set_xlabel('Tr(A)') ax.set_ylabel('Det(A)') ax.set_title('stability plot') # vector field plot ax = axes['3'] x, y = np.meshgrid(np.linspace(xmin, xmax, 10), np.linspace(ymin, ymax, 10)) vx = axx * x + axy * y vy = ayx * x + ayy * y ax.quiver(x,y, vx, vy, units='xy', scale=6, color='g', headwidth=3, width=0.04) # Plot the circle, or fast and slow manifolds if is_rotational: v_1 = np.array(eigen_vects[:,0].real) v_2 = np.array(eigen_vects[:,0].imag) # normalize radius = (xmax - xmin) / 4 norm = max(np.linalg.norm(v_1), np.linalg.norm(v_2)) / radius v_1 /= norm v_2 /= norm plot_circle(v_1, v_2, ax, color=colormap(eigen_vals[0].real)) elif is_critical: v_1 = eigen_vects[:,0] length = (xmax - xmin) * 2 lengths = np.linspace(-length, length, 100) points = v_1[:,np.newaxis] * lengths ax.plot(points[0,:], points[1,:], color=colormap(eigen_vals[0])) else: v_1 = eigen_vects[:,0] v_2 = eigen_vects[:,1] length = (xmax - xmin) * 2 lengths = np.linspace(-length, length, 100) points = v_1[:,np.newaxis] * lengths ax.plot(points[0,:], points[1,:], color=colormap(eigen_vals[0])) points = v_2[:,np.newaxis] * lengths ax.plot(points[0,:], points[1,:], color=colormap(eigen_vals[1])) ax.plot([xmin, xmax], np.zeros(2), color='k', alpha=0.2) ax.plot(np.zeros(2), [ymin, ymax], color='k', alpha=0.2) ax.set_aspect('equal') ax.set_xlim([xmin, xmax]) ax.set_ylim([ymin, ymax]) ax.set_xlabel('$x$') ax.set_ylabel('$\\dot{x}$') ax.set_title('phase portrait') fig.suptitle(title) fig.tight_layout() return fig import tempfile import os import imageio plt.rc('figure', titlesize=16) with tempfile.TemporaryDirectory() as temp_dir: n_frames = 201 omegas = [1.0] * n_frames gammas = (1-np.cos(np.linspace(0, np.pi, n_frames//2)))/2 gammas = list(gammas) + [gammas[-1]] + list(gammas + 1) for i in range(n_frames): omega = omegas[i] gamma = gammas[i] operator_A = np.array([[0, 1], [-omega**2, -2*gamma]]) fig = plot_vector_field(operator_A, title=f"$\\ddot x + 2\\gamma \\dot x + \\omega^2x = 0$,\n$\\omega = {omega:1.1f}$, $\\gamma = {gamma:0.3f}$") filename = os.path.join(temp_dir, f"plot_{i:03d}.png") fig.savefig(filename) plt.close(fig) # Compile images into GIF fps = 12 images = [] for i in range(n_frames): filename = os.path.join(temp_dir, f"plot_{i:03d}.png") images.append(imageio.v2.imread(filename)) imageio.mimsave(f"phase_portrait_omega_{omega:1.1f}.gif", images, duration=1/fps)``` |
Sanasi | |
Manba | Oʻzimning ishim |
Muallif | Cosmia Nebula |
Litsenziyalash
- Siz erkinsiz:
- ulashishga – ishlanmani nusxalash, tarqatish va uzatish
- remiks qilishga – ishni moslashtirishga
- Quyidagi shartlar asosida:
- atribut – Siz tegishli litsenziyaga havolani taqdim etishingiz va oʻzgartirishlar kiritilganligini koʻrsatishingiz kerak. Siz buni har qanday oqilona yoʻl bilan qilishingiz mumkin, lekin litsenziar Sizni yoki Sizning foydalanishingizni ma'qullashini taklif qiladigan tarzda emas.
- bir xil ulashish – Agar Siz materialni remiks qilsangiz, oʻzgartirsangiz yoki unga asoslansangiz, oʻz hissalaringizni asl nusxadagi kabi bir xil yoki mos litsenziya ostida tarqatishingiz kerak.
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original creation by uploader inglizcha
4 Aprel 2023
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Sana/Vaqt | Miniatura | Oʻlchamlari | Foydalanuvchi | Izoh | |
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joriy | 06:24, 5-Aprel 2023 | 1 800 × 1 200 (19,36 MB) | Cosmia Nebula | Uploaded own work with UploadWizard |
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