update

Source/TODEL_poincare_test.py

@@ -0,0 +1,58 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import potentials as pot
+import energies as ene
+import integrator as itg
+import initial_conditions as init
+import poincare_sections as pcs
+
+h = 0.01
+N_inter = 30000
+eps = 1e-2
+
+x_0 = 0.0
+y_vals = np.linspace(0, 0.6, 50)
+E = 0.125  # 1/12
+
+# Initialize lists to store all Poincaré points across different initial conditions
+all_pcs_pos_y = []
+all_pcs_vel_y = []
+
+
+for i in range(len(y_vals)):
+    y0 = y_vals[i]
+    W_part = init.one_part(x_0, y0, 0, 0)
+    POT = pot.hh_potential(W_part)[0]
+    u_0 = np.sqrt(2 * (E - POT))
+    v_0 = 0.0
+
+
+    W_part[1, 0] = u_0
+    W_part[1, 1] = v_0
+
+    # Perform integration
+    pos_t, positions = itg.rk4(0, W_part, h, N_inter, pot.hh_evolution)
+
+    # Extract positions and velocities
+    pos_x = positions[:, 0, 0]
+    pos_y = positions[:, 0, 1]
+    vel_x = positions[:, 1, 0]
+    vel_y = positions[:, 1, 1]
+
+    # Find Poincaré section points for the current initial condition
+    pcs_pos_y, pcs_vel_y = pcs.pcs_find(pos_x, pos_y, vel_x, vel_y)
+
+    # Append the current Poincaré section points to the overall lists
+    all_pcs_pos_y.extend(pcs_pos_y)
+    all_pcs_vel_y.extend(pcs_vel_y)
+
+# Plotting all Poincaré section points on the same graph
+fig, ax = plt.subplots()
+ax.scatter(all_pcs_pos_y, all_pcs_vel_y, s=2, color="C4")
+
+# Set labels and legend
+ax.set_xlabel("coordinate y")
+ax.set_ylabel("velocity v")
+ax.set_title("Combined Poincaré Section for Multiple Initial y0 Values")
+
+plt.show()