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Cdyngrav.py
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# -*- coding: utf-8 -*-
import math
import matplotlib
#sortie du module graphique
#vers des fichiers pdf plutôt que vers fenêtre interactive
matplotlib.use('pdf')
import matplotlib.pyplot as plt
#################################
def smul(nono, lili):
lirev = []
for v in lili:
lirev.append(nono*v)
return lirev
def vsom(l1,l2):
nb = len(l1)
lirev = []
for i in range(nb):
lirev.append(l1[i] + l2[i])
return lirev
def vdif(l1,l2):
nb = len(l1)
lirev = []
for i in range(nb):
lirev.append(l1[i] - l2[i])
return lirev
###########################
def euler(f,y0,z0,h,n):
#initialisations
y , z = y0 , z0
Ly , Lz = [y] , [z]
for i in range(n-1): #n-1 car ini connu
fy = f(y)
y += z*h
z += fy*h
Ly.append(y)
Lz.append(z)
return Ly, Lz
def verlet(f,y0,z0,h,n):
#initialisations
y , z = y0 , z0
Ly , Lz = [y] , [z]
for i in range(n-1):
fy = f(y)
y += z*h + h*h*fy/2 #y suivant
ffy = f(y) # valeur de f au y suivant
z += h*(fy +ffy)/2
Ly.append(y)
Lz.append(z)
return Ly, Lz
def f(u):
omega = 2*math.pi
return -omega*omega*u
############################
def norme2(v):
return (v[0]**2 + v[1]**2 + v[2]**2)**0.5
def force2(m1,p1,m2,p2):
#force par 2 sur 1
G = 6.67e-11
v = vdif(p1,p2)
coeff = G*m1*m2*norme2(v)**(-3)
return smul(coeff,v)
def forceN(j,m,pos):
force = [0.,0.,0.]
N = len(m)
for k in range(N):
if k!= j:
f = force2(m[k],pos[k],m[j],pos[j])
force = vsom(force, f)
return force
def pos_suiv(m,pos,vit,h):
N = len(m)
L = []
for j in range(N):
force = forceN(j,m,pos)
acc_pos1 = smul(h,vit[j])
new_pos = vsom(pos[j],acc_pos1)# Euler
coeff = h*h/(2*m[j])
acc_pos2 = smul(coeff,force) # Verlet
new_pos = vsom(new_pos,acc_pos2)
L.append(new_pos)
return L
def etat_suiv(m,pos,vit,h):
N = len(m)
new_pos = pos_suiv(m,pos,vit,h)
new_vit = []
for j in range(N):
coeff = h/(2*m[j])
f = forceN(j,m,pos)
ff = forceN(j,m,new_pos)
acc_v = vsom(f,ff)
acc_v = smul(coeff,acc_v)
new_vit.append(vsom(vit[j],acc_v))
return new_pos, new_vit
m = [1e12,5e10]
pos = [[0,0,0],[1,0,0]]
vit = [[0,0,0],[0,9,0]]
h = 1e-2
liste_pos = []
for k in range(600):
pos, vit = etat_suiv(m,pos,vit,h)
liste_pos.append(pos)
x0, y0, x1, y1 = [],[],[],[]
X0, Y0, X1, Y1 = [],[],[],[]
M = m[0]+m[1]
c0 = m[0]/M
c1 = m[1]/M
for pos in liste_pos:
xG = c0*pos[0][0] + c1*pos[1][0]
yG = c0*pos[0][1] + c1*pos[1][1]
x0.append(pos[0][0])
X0.append(pos[0][0] - xG)
y0.append(pos[0][1])
Y0.append(pos[0][1] - yG)
x1.append(pos[1][0])
X1.append(pos[1][0] - xG)
y1.append(pos[1][1])
Y1.append(pos[1][1] - yG)
plt.plot(x0,y0,color='red')
plt.plot(x1,y1,color='darkgreen')
plt.title(r'$(x0,y0)\;, \;(x1,y1)$')
plt.savefig('Edyngrav_3.pdf')
plt.clf()
plt.plot(X0,Y0,color='red')
plt.plot(X1,Y1,color='darkgreen')
plt.title(r'$(X0,Y0)\;, \;(X1,Y1)$')
plt.savefig('Edyngrav_4.pdf')
plt.clf()
#plt.show()
"""
print((norme2([1,1,1]))**2)
print(smul(3,[1,2,3]))
print(vsom([1,2,3],[4,5,6]))
ELy, ELz = euler(f,3.,6.,0.03,100)
plt.plot(ELy,ELz,color='darkgreen',linestyle='solid',marker='o')
plt.savefig('Edyngrav_1.pdf')
plt.clf()
VLy, VLz = verlet(f,3.,6.,0.03,100)
plt.plot(VLy,VLz,color='darkgreen',linestyle='solid',marker='o')
plt.savefig('Edyngrav_2.pdf')
"""