Add files via upload

3d_plot.py

@@ -0,0 +1,40 @@
+import math
+import matplotlib.pyplot as plt
+
+m = 1
+g = 1
+l = 1
+gamma = 0.05
+F_0 = 0.7
+omega_d = 0.7
+period = 2 * math.pi / omega_d
+
+
+def alpha(t: float, theta: float, omega: float):
+    return (1 / (m * l)) * (- g * math.sin(theta) - gamma * omega + F_0 * math.cos(omega_d * t))
+
+
+tau = 10000 * 2 * math.pi
+dt = 0.01
+t = 0
+theta = 1
+omega = 0
+thresh = 0
+phases = []
+thetas = []
+omegas = []
+while t < tau:
+    if t >= thresh:
+        phases.append(t % period)
+        thetas.append((theta + math.pi) % (2 * math.pi) - math.pi)
+        omegas.append(omega)
+        thresh += 1
+    omega += alpha(t, theta, omega) * dt
+    theta += omega * dt
+    t += dt
+
+ax = plt.axes(projection='3d')
+ax.scatter(thetas, omegas, phases, s=0.1, c=phases, cmap="plasma")
+plt.show()
+
+

P_Plot.py

@@ -0,0 +1,69 @@
+import math
+import matplotlib.pyplot as plt
+
+m = 1
+g = 1
+l = 1
+gamma = 0.05
+F_0 = 0.7
+omega_d = 0.7
+period = 2 * math.pi / omega_d
+
+
+def alpha(t: float, theta: float, omega: float):
+    return (1 / (m * l)) * (- g * math.sin(theta) - gamma * omega + F_0 * math.cos(omega_d * t))
+
+
+tau = 25000 * 2 * math.pi
+dt = 0.01
+
+t = 0
+theta = 0
+omega = 1
+thresh = 0
+p_thetas = []
+p_omegas = []
+while t < tau:
+    if t >= thresh:
+        thresh += period
+        p_thetas.append((theta + math.pi) % (2 * math.pi) - math.pi)
+        p_omegas.append(omega)
+    omega += alpha(t, theta, omega) * dt
+    theta += omega * dt
+    t += dt
+
+plt.scatter(p_thetas, p_omegas, s=0.1, c='blue')
+
+t = 0
+theta = 0.6
+omega = 0.8
+thresh = 0
+p_thetas = []
+p_omegas = []
+while t < tau:
+    if t >= thresh:
+        thresh += period
+        p_thetas.append((theta + math.pi) % (2 * math.pi) - math.pi)
+        p_omegas.append(omega)
+    omega += alpha(t, theta, omega) * dt
+    theta += omega * dt
+    t += dt
+plt.scatter(p_thetas, p_omegas, s=0.1, c='red')
+
+t = 0
+theta = 1
+omega = 0
+thresh = 0
+p_thetas = []
+p_omegas = []
+while t < tau:
+    if t >= thresh:
+        thresh += period
+        p_thetas.append((theta + math.pi) % (2 * math.pi) - math.pi)
+        p_omegas.append(omega)
+    omega += alpha(t, theta, omega) * dt
+    theta += omega * dt
+    t += dt
+plt.scatter(p_thetas, p_omegas, s=0.1, c='purple')
+
+plt.show()