#!/usr/bin/python # -*- coding:utf-8 -*- """ Hermite integrator """ from os import system import numpy as np from lib.plots import DynamicUpdate from lib.units import * def Update_a(dyn_syst): # update acceleration of bodies in system for body in dyn_syst.bodylist: body.a = np.zeros(3,dtype=np.longdouble) for otherbody in dyn_syst.bodylist: if body != otherbody: rij = np.linalg.norm(body.q - otherbody.q) body.a = body.a - (body.q - otherbody.q) * Ga * otherbody.m / (rij ** 3) def Update_j(dyn_syst): # update jerk of bodies in system for body in dyn_syst.bodylist: body.j = np.zeros(3,dtype=np.longdouble) for otherbody in dyn_syst.bodylist: if body != otherbody: rij = np.linalg.norm(body.q - otherbody.q) deltav = (body.v - otherbody.v) deltar = (body.q - otherbody.q) vr = deltav + 3. * deltar * np.inner(deltav, deltar) / (rij ** 2) body.j = body.j - Ga * otherbody.m / (rij ** 3) * vr def Predict(dyn_syst, dt): # update predicted position and velocities of bodies in system for body in dyn_syst.bodylist: body.qp = body.q + dt * body.v + ((dt ** 2) * body.a / 2.) + ((dt ** 3) * body.j / 6.) body.vp = body.v + dt * body.a + ((dt ** 2) * body.j / 2.) def Update_ap(dyn_syst): # update acceleration of bodies in system for body in dyn_syst.bodylist: body.ap = np.zeros(3,dtype=np.longdouble) for otherbody in dyn_syst.bodylist: if body != otherbody: rij = np.linalg.norm(body.qp - otherbody.qp) body.ap = body.ap - (body.qp - otherbody.qp) * Ga * otherbody.m / (rij ** 3) def Update_jp(dyn_syst): # update jerk of bodies in system for body in dyn_syst.bodylist: body.jp = np.zeros(3,dtype=np.longdouble) for otherbody in dyn_syst.bodylist: if body != otherbody: rij = np.linalg.norm(body.qp - otherbody.qp) deltav = (body.vp - otherbody.vp) deltar = (body.qp - otherbody.qp) vr = deltav + 3. * deltar * np.inner(deltav, deltar) / (rij ** 2) body.jp = body.jp - Ga * otherbody.m / (rij ** 3) * vr def Correct(dyn_syst, dt): # correct position and velocities of bodies in system for body in dyn_syst.bodylist: a2 = (6. * (body.a - body.ap) + dt * (4 * body.j + 2 * body.jp)) / (dt ** 2) a3 = (12. * (body.a - body.ap) + dt * 6. * (body.j + body.jp)) / (dt ** 3) body.q = body.qp + ((dt ** 4) * a2 / 24.) + ((dt ** 5) * a3 / 120.) body.v = body.vp + ((dt ** 3) * a2 / 6.) + ((dt ** 4) * a3 / 24.) def HPC(dyn_syst, dt): # update position and velocities of bodies in system with hermite predictor corrector Update_a(dyn_syst) Update_j(dyn_syst) Predict(dyn_syst, dt) Update_ap(dyn_syst) Update_jp(dyn_syst) Correct(dyn_syst, dt) dyn_syst.time = dyn_syst.time + dt def hermite(dyn_syst, bin_syst, duration, dt, recover_param=False, display=False, savename=None, gif=False): if display: try: system("mkdir tmp") except IOError: system("rm tmp/*") d = DynamicUpdate(dyn_syst) d.launch(dyn_syst.blackstyle) N = np.ceil(duration / dt).astype(int) E = np.zeros(N+1,dtype=np.longdouble) L = np.zeros((N+1, 3),dtype=np.longdouble) sma = np.zeros(N+1,dtype=np.longdouble) ecc = np.zeros(N+1,dtype=np.longdouble) phi = np.zeros(N+1,dtype=np.longdouble) E[0] = dyn_syst.ECOM L[0] = dyn_syst.LCOM sma[0] = bin_syst.smaCOM ecc[0] = bin_syst.eccCOM phi[0] = dyn_syst.phi for j in range(1,N+1): HPC(dyn_syst, dt) E[j] = dyn_syst.ECOM L[j] = dyn_syst.LCOM sma[j] = bin_syst.smaCOM ecc[j] = bin_syst.eccCOM phi[j] = dyn_syst.phi if display and j % 10 == 0: if gif: step = j else: step = None # display progression if len(dyn_syst.bodylist) == 1: d.on_running(step=step, label="{0:.2f} years".format(j*dt/yr)) else: d.on_running(step=step, label="{0:.2f} years".format(j*dt/yr)) if display: d.close() if gif: system("convert -delay 5 -loop 0 tmp/??????.png tmp/temp.gif && rm tmp/??????.png") system("convert tmp/temp.gif -fuzz 10% -layers Optimize plots/{0:s}_dynsyst.gif".format(savename)) if recover_param: return E, L, sma, ecc, phi