#!/usr/bin/python # -*- coding:utf-8 -*- """ Class definition for physical atribute """ from os import system import numpy as np from lib.plots import DynamicUpdate globals()['G'] = 6.67e-11 #Gravitational constant in SI units globals()['Ms'] = 2e30 #Solar mass in kg globals()['au'] = 1.5e11 #Astronomical unit in m class Body: def __init__(self, mass, position, velocity): self.m = mass self.q = position self.v = velocity self.p = velocity*mass self.a = np.zeros(3) self.ap = np.zeros(3) self.j = np.zeros(3) self.jp = np.zeros(3) self.qp = np.zeros(3) self.vp = np.zeros(3) def __repr__(self): # Called upon "print(body)" return "Body of mass: {0:.2f}kg, position: {1}, velocity: {2}".format(self.m, self.p, self.v) def __str__(self): # Called upon "str(body)" return "Body of mass: {0:.2f}kg, position: {1}, velocity: {2}".format(self.m, self.p, self.v) class System: def __init__(self, bodylist): self.bodylist = np.array(bodylist) self.time = 0 def get_masses(self): #return the masses of each object return np.array([body.m for body in self.bodylist]) def get_positions(self): #return the positions of the bodies return np.array([body.q for body in self.bodylist]) def get_velocities(self): #return the positions of the bodies return np.array([body.v for body in self.bodylist]) def get_momenta(self): #return the momenta of the bodies return np.array([body.p for body in self.bodylist]) def Mass(self): #return total system mass mass = 0 for body in self.bodylist: mass = mass + body.m return mass def COM(self): #return center of mass in cartesian np_array coord = np.zeros(3) for body in self.bodylist: coord = coord + body.m*body.q coord = coord/self.Mass() return coord def COMV(self): #return center of mass velocity in cartesian np_array coord = np.zeros(3) for body in self.bodylist: coord = coord + body.p coord = coord/self.Mass() return coord def COMShift(self): #Shift coordinates of bodies in system to COM frame and set COM at rest for body in self.bodylist: body.q = body.q - self.COM() body.p = body.p - self.COMV() return 0 def Lval(self): #return angular momentum of bodies in system L = np.zeros(3) for body in self.bodylist: L = L + np.cross(body.q,body.p) return L def Eval(self): #return total energy of bodies in system T = 0 W = 0 for body in self.bodylist: T = T + 1./2.*body.m*np.linalg.norm(body.v)**2 for otherbody in self.bodylist: if body != otherbody: rij = np.linalg.norm(body.q-otherbody.q) W = W - G*body.m*otherbody.m/rij return T + W def __repr__(self): # Called upon "print(system)" return str([print(body) for body in self.bodylist]) def __str__(self): # Called upon "str(system)" return str([str(body) for body in self.bodylist]) def Update_a(self): #update acceleration of bodies in system for body in self.bodylist: body.a = np.zeros(3) for otherbody in self.bodylist: if body != otherbody: rij = np.linalg.norm(body.q-otherbody.q) body.a = body.a - (body.q-otherbody.q)*G*otherbody.m/(rij**3) return 1 def Update_j(self): #update jerk of bodies in system for body in self.bodylist: body.j = np.zeros(3) for otherbody in self.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 - G*otherbody.m/(rij**3)*vr return 1 def Predict(self,dt): # update predicted position and velocities of bodies in system for body in self.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.) #print("v=",body.v," vp=" ,body.vp) return 1 def Update_ap(self): #update acceleration of bodies in system for body in self.bodylist: body.ap = np.zeros(3) for otherbody in self.bodylist: if body != otherbody: rij = np.linalg.norm(body.qp-otherbody.qp) body.ap = body.ap - (body.qp-otherbody.qp)*G*otherbody.m/(rij**3) return 1 def Update_jp(self): #update jerk of bodies in system for body in self.bodylist: body.jp = np.zeros(3) for otherbody in self.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 - G*otherbody.m/(rij**3)*vr return 1 def Correct(self,dt): # correct position and velocities of bodies in system for body in self.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.) return 1 def HPC(self, dt): # update position and velocities of bodies in system with hermite predictor corrector self.COMShift() self.Update_a() self.Update_j() self.Predict(dt) self.Update_ap() self.Update_jp() self.Correct(dt) self.time = self.time + dt for body in self.bodylist: body.p = body.v*body.m def hermite(self, duration, dt, recover_param=False, display=False): if display: try: system("mkdir tmp") except IOError: system("rm tmp/*") d = DynamicUpdate() d.on_launch() N = np.ceil(duration/dt).astype(int) E = np.zeros(N) L = np.zeros((N,3)) for j in range(N): self.HPC(dt) E[j] = self.Eval() L[j] = self.Lval() if display: # display progression q_array = self.get_positions() if len(self.bodylist) == 1: d.on_running(q_array[0], q_array[1], q_array[2], step=j, label="step {0:d}/{1:d}".format(j,N)) else: d.on_running(q_array[:,0], q_array[:,1], q_array[:,2], step=j, label="step {0:d}/{1:d}".format(j,N)) if recover_param: return E, L