249 lines
8.7 KiB
Python
Executable File
249 lines
8.7 KiB
Python
Executable File
#!/usr/bin/python
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# -*- coding:utf-8 -*-
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"""
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Class definition for physical atribute
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"""
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from os import system
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import numpy as np
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from lib.plots import DynamicUpdate
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globals()['G'] = 6.67e-11 #Gravitational constant in SI units
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globals()['Ms'] = 2e30 #Solar mass in kg
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globals()['au'] = 1.5e11 #Astronomical unit in m
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class Body:
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def __init__(self, mass, position, velocity):
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self.m = mass
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self.q = position
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self.v = velocity
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self.p = velocity*mass
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self.a = np.zeros(3)
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self.ap = np.zeros(3)
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self.j = np.zeros(3)
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self.jp = np.zeros(3)
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self.qp = np.zeros(3)
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self.vp = np.zeros(3)
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def __repr__(self): # Called upon "print(body)"
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return "Body of mass: {0:.2e}kg, position: {1}, velocity: {2}".format(self.m, self.q, self.v)
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def __str__(self): # Called upon "str(body)"
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return "Body of mass: {0:.2e}kg".format(self.m)
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class System:
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def __init__(self, bodylist):
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self.bodylist = np.array(bodylist)
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self.time = 0
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def get_masses(self): #return the masses of each object
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return np.array([body.m for body in self.bodylist])
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def get_positions(self): #return the positions of the bodies
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return np.array([body.q for body in self.bodylist])
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def get_velocities(self): #return the positions of the bodies
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return np.array([body.v for body in self.bodylist])
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def get_momenta(self): #return the momenta of the bodies
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return np.array([body.p for body in self.bodylist])
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def Mass(self): #return total system mass
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mass = 0
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for body in self.bodylist:
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mass = mass + body.m
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return mass
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def COM(self): #return center of mass in cartesian np_array
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coord = np.zeros(3)
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for body in self.bodylist:
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coord = coord + body.m*body.q
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coord = coord/self.Mass()
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return coord
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def COMV(self): #return center of mass velocity in cartesian np_array
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coord = np.zeros(3)
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for body in self.bodylist:
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coord = coord + body.p
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coord = coord/self.Mass()
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return coord
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def COMShift(self): #Shift coordinates of bodies in system to COM frame and set COM at rest
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for body in self.bodylist:
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body.q = body.q - self.COM()
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body.p = body.p - self.COMV()
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return 0
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def Lval(self): #return angular momentum of bodies in system
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L = np.zeros(3)
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for body in self.bodylist:
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L = L + np.cross(body.q,body.p)
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return L
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def Eval(self): #return total energy of bodies in system
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T = 0
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W = 0
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for body in self.bodylist:
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T = T + 1./2.*body.m*np.linalg.norm(body.v)**2
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for otherbody in self.bodylist:
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if body != otherbody:
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rij = np.linalg.norm(body.q-otherbody.q)
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W = W - G*body.m*otherbody.m/rij
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return T + W
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def Drift(self, dt):
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for body in self.bodylist:
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body.q = body.q + dt*body.v
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def Kick(self, dt):
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for body in self.bodylist:
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body.a = np.zeros(3)
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for otherbody in self.bodylist:
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if body != otherbody:
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rij = np.linalg.norm(body.q-otherbody.q)
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body.a = body.a - (body.q-otherbody.q)*G*otherbody.m/(rij**3)
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body.v = body.v + dt*body.a
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def LP(self, dt):
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self.COMShift()
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self.Drift(dt/2)
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self.Kick(dt)
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self.Drift(dt/2)
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self.time = self.time + dt
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for body in self.bodylist:
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body.p = body.v*body.m
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def leapfrog(self, duration, dt, recover_param=False, display=False):
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if display:
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try:
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system("mkdir tmp")
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except IOError:
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system("rm tmp/*")
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d = DynamicUpdate(self)
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d.on_launch()
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N = np.ceil(duration/dt).astype(int)
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E = np.zeros(N)
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L = np.zeros((N,3))
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for j in range(N):
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self.LP(dt)
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E[j] = self.Eval()
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L[j] = self.Lval()
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if display and j%100==0:
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# display progression
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if len(self.bodylist) == 1:
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d.on_running(self, step=j, label="step {0:d}/{1:d}".format(j,N))
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else:
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d.on_running(self, step=j, label="step {0:d}/{1:d}".format(j,N))
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if display:
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system("convert -delay 5 -loop 0 tmp/??????.png tmp/temp.gif && rm tmp/??????.png")
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system("convert tmp/temp.gif -fuzz 10% -layers Optimize plots/dynsyst.gif")# && rm tmp/temp.gif")
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if recover_param:
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return E, L
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def Update_a(self): #update acceleration of bodies in system
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for body in self.bodylist:
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body.a = np.zeros(3)
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for otherbody in self.bodylist:
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if body != otherbody:
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rij = np.linalg.norm(body.q-otherbody.q)
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body.a = body.a - (body.q-otherbody.q)*G*otherbody.m/(rij**3)
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def Update_j(self): #update jerk of bodies in system
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for body in self.bodylist:
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body.j = np.zeros(3)
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for otherbody in self.bodylist:
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if body != otherbody:
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rij = np.linalg.norm(body.q-otherbody.q)
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deltav = (body.v-otherbody.v)
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deltar = (body.q-otherbody.q)
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vr = deltav + 3.*deltar*np.inner(deltav,deltar)/(rij**2)
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body.j = body.j - G*otherbody.m/(rij**3)*vr
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def Predict(self,dt): # update predicted position and velocities of bodies in system
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for body in self.bodylist:
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body.qp = body.q +dt*body.v+((dt**2)*body.a/2.)+((dt**3)*body.j/6.)
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body.vp = body.v + dt*body.a + ((dt**2)*body.j/2.)
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def Update_ap(self): #update acceleration of bodies in system
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for body in self.bodylist:
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body.ap = np.zeros(3)
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for otherbody in self.bodylist:
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if body != otherbody:
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rij = np.linalg.norm(body.qp-otherbody.qp)
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body.ap = body.ap - (body.qp-otherbody.qp)*G*otherbody.m/(rij**3)
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def Update_jp(self): #update jerk of bodies in system
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for body in self.bodylist:
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body.jp = np.zeros(3)
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for otherbody in self.bodylist:
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if body != otherbody:
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rij = np.linalg.norm(body.qp-otherbody.qp)
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deltav = (body.vp-otherbody.vp)
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deltar = (body.qp-otherbody.qp)
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vr = deltav + 3.*deltar*np.inner(deltav,deltar)/(rij**2)
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body.jp = body.jp - G*otherbody.m/(rij**3)*vr
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def Correct(self,dt): # correct position and velocities of bodies in system
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for body in self.bodylist:
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a2 = (6.*(body.a-body.ap)+dt*(4*body.j+2*body.jp))/(dt**2)
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a3 = (12. * (body.a - body.ap) + dt * 6. * (body.j + body.jp)) / (dt ** 3)
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body.q = body.qp +((dt**4)*a2/24.) + ((dt**5)*a3/120.)
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body.v = body.vp +((dt**3)*a2/6.) + ((dt**4)*a3/24.)
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def HPC(self, dt): # update position and velocities of bodies in system with hermite predictor corrector
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self.COMShift()
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self.Update_a()
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self.Update_j()
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self.Predict(dt)
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self.Update_ap()
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self.Update_jp()
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self.Correct(dt)
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self.time = self.time + dt
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for body in self.bodylist:
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body.p = body.v*body.m
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def hermite(self, duration, dt, recover_param=False, display=False):
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if display:
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try:
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system("mkdir tmp")
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except IOError:
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system("rm tmp/*")
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d = DynamicUpdate(self)
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d.on_launch()
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N = np.ceil(duration/dt).astype(int)
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E = np.zeros(N)
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L = np.zeros((N,3))
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for j in range(N):
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self.HPC(dt)
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E[j] = self.Eval()
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L[j] = self.Lval()
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if display and j%100==0:
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# display progression
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if len(self.bodylist) == 1:
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d.on_running(self, step=j, label="step {0:d}/{1:d}".format(j,N))
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else:
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d.on_running(self, step=j, label="step {0:d}/{1:d}".format(j,N))
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if display:
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system("convert -delay 5 -loop 0 tmp/??????.png tmp/temp.gif && rm tmp/??????.png")
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system("convert tmp/temp.gif -fuzz 10% -layers Optimize plots/dynsyst.gif")# && rm tmp/temp.gif")
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if recover_param:
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return E, L
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def __repr__(self): # Called upon "print(system)"
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return str([print(body) for body in self.bodylist])
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def __str__(self): # Called upon "str(system)"
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return str([str(body) for body in self.bodylist])
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