added chaotic version of the evolution test

Source/test_evolution_chaotic.py

@@ -0,0 +1,94 @@
+#!/usr/bin/env python
+"""
+Test: Evolution
+
+Evolve a particle with a given energy in a potential and show the result path
+followed by the particle in a given time.
+
+@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
+@ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
+                de Strasbourg, UMR 7550, F-67000 Strasbourg, France
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+test_evolution.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
+
+"""
+
+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
+
+if "YII_1" in plt.style.available: plt.style.use("YII_1")
+# Loading matplotlib style...
+
+# Constants
+N_grid = 5000
+h = 0.01
+N_inter = 5000
+eps = 1e-2
+
+x_0 = 0.3
+y_0 = 0.1
+E = 1/6
+
+# Main
+if __name__ == "__main__":
+    W_part = init.one_part(x_0, y_0,0,0)
+    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
+
+    pos_t, positions = itg.rk4(0, W_part, h, N_inter, pot.hh_evolution)
+
+    pos_x = positions[:,0,0]
+    pos_y = positions[:,0,1]
+    vel_x = positions[:,1,0]
+    vel_y = positions[:,1,1]
+
+    W_grid = init.mesh_grid(N_grid)
+    X_grid = W_grid[0]
+    Y_grid = W_grid[1]
+    potential = pot.hh_potential(W_grid, position_only=True)
+
+    fig, ax = plt.subplots(1)
+
+    pcm = ax.pcolormesh(X_grid, Y_grid, potential)
+    line = ax.plot(pos_x, pos_y, color="C3")
+    fig.colorbar(pcm, label="potential")
+
+    ax.set_xlabel("$x$")
+    ax.set_ylabel("$y$")
+    ax.set_aspect("equal")
+
+    plt.savefig("Figs/evolution_chaotic.png")
+
+    plt.show(block=True)
+
+