Kozlova 204

oscillator.py

@@ -0,0 +1,78 @@
+#!/usr/bin/env python
+# coding: utf-8
+
+# In[24]:
+
+
+import matplotlib.pyplot as plt
+import numpy as np
+from celluloid import Camera
+from IPython.display import HTML
+
+delta = 0.5; w_0 = 2*np.pi/5
+
+length = 10
+
+def f(u, t):
+    return np.array([
+        u[1],
+        - 2 * delta * u[1] - w_0 ** 2 * np.sin(u[0])
+    ])
+
+t_0 = 0; t_final = 50
+
+M = 1000
+
+tau = (t_final - t_0)/M
+t = np.linspace(t_0, t_final, M + 1)
+
+phi = np.zeros((M + 1, 2))
+
+phi[0] = [5*np.pi/6, 0]
+
+for n in range(M):
+    k1 = f(phi[n], t[n])
+    k2 = f(phi[n] + tau * k1/2, t[n]  + tau/2)
+    k3 = f(phi[n] + tau * k2/2, t[n] + tau/2)
+    k4 = f(phi[n] + tau * k3, t[n] + tau)
+    phi[n + 1] = phi[n] + tau / 6 * (k1 + 2*k2 + 2*k3 + k4)
+
+X = -length * np.sin(phi)
+X = X[:, 0]
+
+Y = -length * np.cos(phi)
+Y = Y[:, 0]
+
+circle_r = np.linspace(- np.pi * 50, 0, 50 * 50)
+circle_l = np.linspace(0, np.pi * 50, 50 * 50)
+
+fig, axs = plt.subplots(figsize=(8, 8), ncols=2, nrows=2, layout='tight')
+
+axs[0][0].set_xlim((-11, 11))
+axs[0][0].set_ylim((-11, 11))
+
+camera = Camera(fig)
+for i in range(0, phi.shape[0], 5):
+    axs[0][0].plot([0, X[i]], [0, Y[i]], c='red')
+    axs[0][0].scatter([X[i]], [Y[i]], c='red')
+    axs[0][1].scatter(t[i], phi[i, 0], c='red')
+    axs[1][0].scatter(t[i], phi[i, 1], c='red')
+    axs[1][1].scatter(phi[i, 0], phi[i, 1], c='red')
+    camera.snap()
+anim = camera.animate()
+HTML(anim.to_html5_video())
+
+#axs[0][0].scatter([0], [0], c='black')
+#axs[0][0].plot([0, 0], [-10, 0], 'b--')
+axs[0][1].plot(t, phi[:, 0], c='blue')
+axs[1][0].plot(t, phi[:, 1], c='red')
+axs[1][1].plot(phi[:, 0], phi[:, 1], c='green')
+
+HTML(anim.to_html5_video())
+
+
+# In[ ]:
+
+
+
+