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102 lines
3.4 KiB
Python
102 lines
3.4 KiB
Python
#!/usr/bin/env python
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"""
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Poincaré Sections
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Computes the Poincaré Sections
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@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
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@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique
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de Strasbourg, UMR 7550, F-67000 Strasbourg, France
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@ Date: 2025-01-01
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Licence:
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Order and Chaos in a 2D potential
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Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
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Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
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poincare_sections.py
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Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
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Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see https://www.gnu.org/licenses/.
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"""
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import numpy as np
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def pcs_find(pos_x, pos_y, vel_x, vel_y):
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"""Find Poincaré sections (PCS; x = 0)
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@ params:
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- pos_x: position along the x axis
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- pos_y: position along the y axis
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- pos_x: velocity along the x axis
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- pos_y: velocity along the y axis
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@ returns: (tuple)
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- pcs_pos_y: position of the points in the PCS along the y axis
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- pcs_vel_y: velocity of the points in the PCS along the y axis
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"""
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if np.ndim(pos_x) == 1:
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pos_x = np.array([pos_x])
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pos_y = np.array([pos_y])
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vel_x = np.array([vel_x])
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vel_y = np.array([vel_y])
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pcs_pos_y = []
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pcs_vel_y = []
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for j in range(len(pos_x[0])): # for each particle
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i = 0
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x = pos_x[:,j]
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y = pos_y[:,j]
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u = vel_x[:,j]
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v = vel_y[:,j]
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while i < len(x) - 1:
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if x[i] * x[i+1] < 0:
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y0 = y[i] \
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+ (y[i+1] - y[i])/(x[i+1] - x[i]) \
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* (0 - x[i])
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v0 = v[i] \
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+ (v[i+1] - v[i])/(x[i+1] - x[i])\
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* (0 - x[i])
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pcs_pos_y.append(y0)
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pcs_vel_y.append(v0)
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i += 1
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return pcs_pos_y, pcs_vel_y
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def pcs_find_legacy(pos_x, pos_y, vel_x, vel_y):
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"""DEPRECIATED - DO NOT USE
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Depreciated legacy function that should not be used
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"""
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if np.ndim(pos_x) == 1:
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pos_x = np.array([pos_x])
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pos_y = np.array([pos_y])
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vel_x = np.array([vel_x])
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vel_y = np.array([vel_y])
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pcs_pos_y = []
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pcs_vel_y = []
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for j in range(len(pos_x)): # for each particle
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i = 0
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x = pos_x[j]
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y = pos_y[j]
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u = vel_x[j]
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v = vel_y[j]
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while i < len(x) - 1:
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if x[i] * x[i+1] < 0:
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y0 = y[i] \
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+ (y[i+1] - y[i])/(x[i+1] - x[i]) \
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* (0 - x[i])
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v0 = v[i] \
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+ (v[i+1] - v[i])/(x[i+1] - x[i])\
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* (0 - x[i])
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pcs_pos_y.append(y0)
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pcs_vel_y.append(v0)
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i += 1
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return pcs_pos_y, pcs_vel_y
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