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RK4_def_class.py
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#!/usr/bin/env python
# coding: utf-8
# In[1]:
import numpy as np
from Accelerations import *
from Schwarschild_function import schwarzschild_2
# In[2]:
a = 1
b = 0.05
Mbh = 1e-1
# In[3]:
class MultipleStars:
def __init__(self, number_stars, a, b):
self.number_stars = number_stars
self.a = a
self.b = b
self.x, self.y, self.z, self.vx, self.vy, self.vz = schwarzschild_2(self.a, self.b, self.number_stars)
def RK4 (self, h, N):
position3D = np.zeros((3, self.number_stars, int(N//h)+1))
velocity3D = np.zeros((3, self.number_stars, int(N//h)+1))
for j in range(0, self.number_stars):
i = 0
x = self.x[j]
y = self.y[j]
z = self.z[j]
vx = self.vx[j]
vy = self.vy[j]
vz = self.vz[j]
for k in np.arange(0,N,h):
#order1
kx1 = vx*h
ky1 = vy*h
kz1 = vz*h
ku1 = h*acceleration_x( x, y, z)
kv1 = h*acceleration_y( x, y, z)
kw1 = h*acceleration_z( x, y, z)
#order2
kx2 = (vx+0.5*ku1)*h
ky2 = (vy+0.5*kv1)*h
kz2 = (vz+0.5*kw1)*h
ku2 = h*acceleration_x( x+kx1/2, y+ky1/2, z+kz1/2)
kv2 = h*acceleration_y( x+kx1/2, y+ky1/2, z+kz1/2)
kw2 = h*acceleration_z( x+kx1/2, y+ky1/2, z+kz1/2)
#order3
kx3 = (vx+0.5*ku2)*h
ky3 = (vy+0.5*kv2)*h
kz3 = (vz+0.5*kw2)*h
ku3 = h*acceleration_x( x+kx2/2, y+ky2/2, z+kz2/2)
kv3 = h*acceleration_y( x+kx2/2, y+ky2/2, z+kz2/2)
kw3 = h*acceleration_z( x+kx2/2, y+ky2/2, z+kz2/2)
#order4
kx4 = (vx+ku3)*h
ky4 = (vy+kv3)*h
kz4 = (vz+kw3)*h
ku4 = h*acceleration_x( x+kx3, y+ky3, z+kz3)
kv4 = h*acceleration_y( x+kx3, y+ky3, z+kz3)
kw4 = h*acceleration_z( x+kx3, y+ky3, z+kz3)
#calculation of the positions
x += (kx1+2*kx2+2*kx3+kx4)/6.
y += (ky1+2*ky2+2*ky3+ky4)/6.
z += (kz1+2*kz2+2*kz3+kz4)/6.
#calculation of the velocities
vx += (ku1+2*ku2+2*ku3+ku4)/6.
vy += (kv1+2*kv2+2*kv3+kv4)/6.
vz += (kw1+2*kw2+2*kw3+kw4)/6.
#adding to the list to get the informations
position3D[0,j,i]=x
position3D[1,j,i]=y
position3D[2,j,i]=z
velocity3D[0,j,i]=vx
velocity3D[1,j,i]=vy
velocity3D[2,j,i]=vz
i=i+1
return position3D, velocity3D
def RK4_perturbation (self, h, N, X, Y, Z):
position3D = np.zeros((3, self.number_stars, int(N//h)+1))
velocity3D = np.zeros((3, self.number_stars, int(N//h)+1))
for j in range(0, self.number_stars):
i = 0
x = self.x[j]
y = self.y[j]
z = self.z[j]
vx = self.vx[j]
vy = self.vy[j]
vz = self.vz[j]
x_bh = X[0]
y_bh = Y[0]
z_bh = Z[0]
for k in np.arange(0,N,h):
#order1
kx1 = vx*h
ky1 = vy*h
kz1 = vz*h
ku1 = h*acceleration_x_star( x, y, z, X[i], Y[i], Z[i])
kv1 = h*acceleration_y_star( x, y, z, X[i], Y[i], Z[i])
kw1 = h*acceleration_z_star( x, y, z, X[i], Y[i], Z[i])
#order2
kx2 = (vx+0.5*ku1)*h
ky2 = (vy+0.5*kv1)*h
kz2 = (vz+0.5*kw1)*h
ku2 = h*acceleration_x_star( x+kx1/2, y+ky1/2, z+kz1/2, X[i], Y[i], Z[i])
kv2 = h*acceleration_y_star( x+kx1/2, y+ky1/2, z+kz1/2, X[i], Y[i], Z[i])
kw2 = h*acceleration_z_star( x+kx1/2, y+ky1/2, z+kz1/2, X[i], Y[i], Z[i])
#order3
kx3 = (vx+0.5*ku2)*h
ky3 = (vy+0.5*kv2)*h
kz3 = (vz+0.5*kw2)*h
ku3 = h*acceleration_x_star( x+kx2/2, y+ky2/2, z+kz2/2, X[i], Y[i], Z[i])
kv3 = h*acceleration_y_star( x+kx2/2, y+ky2/2, z+kz2/2, X[i], Y[i], Z[i])
kw3 = h*acceleration_z_star( x+kx2/2, y+ky2/2, z+kz2/2, X[i], Y[i], Z[i])
#order4
kx4 = (vx+ku3)*h
ky4 = (vy+kv3)*h
kz4 = (vz+kw3)*h
ku4 = h*acceleration_x_star( x+kx3, y+ky3, z+kz3, X[i], Y[i], Z[i])
kv4 = h*acceleration_y_star( x+kx3, y+ky3, z+kz3, X[i], Y[i], Z[i])
kw4 = h*acceleration_z_star( x+kx3, y+ky3, z+kz3, X[i], Y[i], Z[i])
#calculation of the positions
x += (kx1+2*kx2+2*kx3+kx4)/6.
y += (ky1+2*ky2+2*ky3+ky4)/6.
z += (kz1+2*kz2+2*kz3+kz4)/6.
#calculation of the velocities
vx += (ku1+2*ku2+2*ku3+ku4)/6.
vy += (kv1+2*kv2+2*kv3+kv4)/6.
vz += (kw1+2*kw2+2*kw3+kw4)/6.
#adding to the list to get the informations
position3D[0,j,i]=x
position3D[1,j,i]=y
position3D[2,j,i]=z
velocity3D[0,j,i]=vx
velocity3D[1,j,i]=vy
velocity3D[2,j,i]=vz
i=i+1
return position3D, velocity3D
# In[4]:
def RK4_BH (x, y, z, vx, vy, vz, h, N):
X = []
Y = []
Z = []
Vx = []
Vy = []
Vz = []
for k in np.arange (0,N,h):
#order1
kx1 = vx*h
ky1 = vy*h
kz1 = vz*h
ku1 = h*acceleration_x_BH( x, y, z)
kv1 = h*acceleration_y_BH( x, y, z)
kw1 = h*acceleration_z_BH( x, y, z)
#order2
kx2 = (vx+0.5*ku1)*h
ky2 = (vy+0.5*kv1)*h
kz2 = (vz+0.5*kw1)*h
ku2 = h*acceleration_x_BH( x+kx1/2, y+ky1/2, z+kz1/2)
kv2 = h*acceleration_y_BH( x+kx1/2, y+ky1/2, z+kz1/2)
kw2 = h*acceleration_z_BH( x+kx1/2, y+ky1/2, z+kz1/2)
#order3
kx3 = (vx+0.5*ku2)*h
ky3 = (vy+0.5*kv2)*h
kz3 = (vz+0.5*kw2)*h
ku3 = h*acceleration_x_BH( x+kx2/2, y+ky2/2, z+kz2/2)
kv3 = h*acceleration_y_BH( x+kx2/2, y+ky2/2, z+kz2/2)
kw3 = h*acceleration_z_BH( x+kx2/2, y+ky2/2, z+kz2/2)
#order4
kx4 = (vx+ku3)*h
ky4 = (vy+kv3)*h
kz4 = (vz+kw3)*h
ku4 = h*acceleration_x_BH( x+kx3, y+ky3, z+kz3)
kv4 = h*acceleration_y_BH( x+kx3, y+ky3, z+kz3)
kw4 = h*acceleration_z_BH( x+kx3, y+ky3, z+kz3)
#calcul of the positions
x += (kx1+2*kx2+2*kx3+kx4)/6.
y += (ky1+2*ky2+2*ky3+ky4)/6.
z += (kz1+2*kz2+2*kz3+kz4)/6.
#calcul of the celerities
vx += (ku1+2*ku2+2*ku3+ku4)/6.
vy += (kv1+2*kv2+2*kv3+kv4)/6.
vz += (kw1+2*kw2+2*kw3+kw4)/6.
#adding to the list to get the informations
X.append(x)
Y.append(y)
Z.append(z)
Vx.append(vx)
Vy.append(vy)
Vz.append(vz)
return X,Y,Z