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124 lines
3.7 KiB
Python
124 lines
3.7 KiB
Python
#!/usr/bin/env python
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"""
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Potentials
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Functions of the different potentials (and their derivatives for the evolution)
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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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potentials.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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MAX_VAL = 1e3
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def kepler_potential(W_grid: np.ndarray,
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position_only: bool = False) -> np.ndarray:
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"""Computes the Kepler potential: V(R) = -G*m1*m2/R
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(assuming G = 1, m1 = 1, m2 = 1)
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assuming the point mass at (x = 0, y = 0).
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@params:
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- W: Phase-space vector
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- position_only: True if W is np.array([X, Y])
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@returns:
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- computed potential
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"""
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if position_only:
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X = W_grid[0]
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Y = W_grid[1]
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else:
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X = W_grid[0,0]
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Y = W_grid[0,1]
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# If X or Y is not an array (or a list), but rather a scalar, then we
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# create a list of one element so that it can work either way
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if np.ndim(X) == 0: X = np.array([X])
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if np.ndim(Y) == 0: Y = np.array([Y])
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R = np.sqrt(X**2 + Y**2)
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return -1/R
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def kepler_evolution(t: np.ndarray, W: np.ndarray):
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"""Computes the evolution from the Kepler potential derivative
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@params
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- t: Time (not used)
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- W: Phase space vector
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&returns
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- dot W: Time derivative of the phase space vector
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"""
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X = W[0 ,0]
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Y = W[0, 1]
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U = W[1, 0]
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V = W[1, 1]
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R = np.sqrt(X**2 + Y**2)
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DX = U
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DY = V
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DU = -X/R**3
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DV = -Y/R**3
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return np.array([[DX, DY], [DU, DV]])
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def hh_potential(W_grid: np.ndarray,
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position_only=False) -> np.ndarray:
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"""Computes the Hénon-Heiles potential.
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@params:
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- W: Phase-space vector
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- position_only: True if W is np.array([X, Y])
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@returns:
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- POT: Potential
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"""
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if position_only:
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X = W_grid[0]
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Y = W_grid[1]
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else:
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X = W_grid[0, 0]
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Y = W_grid[0, 1]
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# If X or Y is not an array (or a list), but rather a scalar, then we
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# create a list of one element so that it can work either way
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if np.ndim(X) == 0: X = np.array([X])
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if np.ndim(Y) == 0: Y = np.array([Y])
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POT = (X**2 + Y**2 + 2*X**2*Y - 2*Y**3/3)/2
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return POT
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def hh_evolution(t: np.ndarray, W: np.ndarray):
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"""Computes the evolution from the HH potential derivative
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@params
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- t: Time (not used)
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- W: Phase space vector
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&returns
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- dot W: Time derivative of the phase space vector
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"""
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X = W[0 ,0]
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Y = W[0, 1]
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U = W[1, 0]
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V = W[1, 1]
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DX = U
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DY = V
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DU = -(2*X*Y + X)
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DV = -(X**2 - Y**2 + Y)
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return np.array([[DX, DY], [DU, DV]])
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