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3Body2Py_1f2m.py
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#! /usr/bin/env python
# -*- coding: utf-8 -*-
# Newton laws Integrator and real time display
# Author: David Sousa [email protected]
# Method: Velocity Verlet
# License: Creative Commons
# 1 fixed and two mobile bodies
# Importing Libraries ##################################################
import pygame
import sys
from pygame.locals import *
import numpy as np
from math import pi, sqrt
# Simulation - Initial Data ############################################
# Uncomment the initial data set you want, or create your own.
# initial
#d1=(1.,1.,1.,-1,6.29)
#d2=(0.1,2.,0.,-1,0.1)
#d3=(0.5e-3,40)
#d4=(1.0)
# three body colision!
#d1=(1.,0.,1.,-1,6.29)
#d2=(0.01,1.,1.5,-3.5,12)
#d3=(0.5e-3,40)
#d4=(1.0)
# Irregular moon
#d1=(1.,1.,0.,-1,6.29)
#d2=(0.01,1.5,0.0,-3.5,12)
#d3=(0.5e-3,40)
#d4=(1.0)
# crazy dance
#d1=(1.00,3.0,0.0,0.0,3.0)
#d2=(0.01,3.5,0.0,0.0,6.0)
#d3=(0.5e-3,40)
#d4=(1.0)
# almost there...
#d1=(1.00,3.0,0.0,0.0,3.0)
#d2=(0.01,3.25,0.0,0.0,9.0)
#d3=(0.5e-3,40)
#d4=(1.0)
# PERFECT!
d1=(1.00,3.0,0.0,0.0,3.0)
d2=(0.01,3.25,0.0,0.0,15.0)
d3=(0.5e-3,40)
d4=(1.0)
m1,x01,y01,vx01,vy01 = d1
m2,x02,y02,vx02,vy02 = d2
h,tf = d3
M = d4
G=-4*pi**2
# E = K1 + V1 + K2 + V2 + V12
E0 = m1*(0.5*(vx01**2 + vy01**2) + G*M/sqrt(x01** 2+ y01**2))
E0+= m2*(0.5*(vx02**2 + vy02**2) + G*M/sqrt(x02** 2+ y02**2))
E0+= G*m1*m2/sqrt((x01-x02)**2+(y01-y02)**2)
# Initializing variables ###############################################
# Main Loop:
# Data: x[n] , v[n]
# Calculate a[n] = -(1/m)*(d/dx) V{ x[n] } = (1/m)F{ x[n] }
# x[n+1] = x[n] + h*v[n] + h*h/2*a[n]
# Calculate a[n+1] = -(1/m)*(d/dx) V{ x[n+1] } = (1/m)F{ x[n+1] }
# v[n+1] = v[n] + h*(a[n+1] + a[n])/2
x1= [x01]; y1= [y01]; vx1=[vx01]; vy1=[vy01]
x2= [x02]; y2= [y02]; vx2=[vx02]; vy2=[vy02]
E=[E0]; e=[0.0]
i=0
ax1=[ G*M*x1[i]/(x1[i]**2+y1[i]**2)**1.5 + G*m2*(x1[i]-x2[i])/((x1[i]-x2[i])**2+(y1[i]-y2[i])**2)**1.5]
ay1=[ G*M*y1[i]/(x1[i]**2+y1[i]**2)**1.5 + G*m2*(y1[i]-y2[i])/((x1[i]-x2[i])**2+(y1[i]-y2[i])**2)**1.5]
ax2=[ G*M*x2[i]/(x1[i]**2+y1[i]**2)**1.5 + G*m1*(x2[i]-x1[i])/((x2[i]-x1[i])**2+(y2[i]-y1[i])**2)**1.5]
ay2=[ G*M*y2[i]/(x1[i]**2+y1[i]**2)**1.5 + G*m1*(y2[i]-y1[i])/((x2[i]-x1[i])**2+(y2[i]-y1[i])**2)**1.5]
t=np.arange(0,tf,h)
# Initialize the screen ################################################
w=255
red,green,blue,white,black = (w,0,0),(0,w,0),(0,0,w),(w,w,w),(0,0,0)
sizex =600; sizey =600
sizeqx = 2; sizeqy = 2
margin=15
pygame.init()
clock = pygame.time.Clock()
screen = pygame.display.set_mode((sizex,sizey))
myfont = pygame.font.SysFont("Sans", 20)
pygame.display.set_caption( 'Sun + 2 Planets by DavidSousa' )
score=pygame.Rect(margin,550,sizex-2*margin,40)
gameover=pygame.Rect(200,200,300,50)
screen.fill((200,200,200))
pygame.draw.rect(screen, white, (margin,margin,sizex-2*margin, sizey-2*margin-50), 0)
pygame.draw.circle(screen, red, (sizex//2-5, sizey//2-5), 10)
pygame.display.update()
collide=-1
# Integration process ##################################################
for i in xrange(0,len(t)-1):
x1.append( x1[i] + h*vx1[i] + h*h*ax1[i]/2 )
y1.append( y1[i] + h*vy1[i] + h*h*ay1[i]/2 )
x2.append( x2[i] + h*vx2[i] + h*h*ax2[i]/2 )
y2.append( y2[i] + h*vy2[i] + h*h*ay2[i]/2 )
ax1.append( G*M*x1[i+1]/(x1[i+1]**2+y1[i+1]**2)**1.5 + G*m2*(x1[i+1]-x2[i+1])/((x1[i+1]-x2[i+1])**2+(y1[i+1]-y2[i+1])**2)**1.5 )
ay1.append( G*M*y1[i+1]/(x1[i+1]**2+y1[i+1]**2)**1.5 + G*m2*(y1[i+1]-y2[i+1])/((x1[i+1]-x2[i+1])**2+(y1[i+1]-y2[i+1])**2)**1.5 )
ax2.append( G*M*x2[i+1]/(x1[i+1]**2+y1[i+1]**2)**1.5 + G*m1*(x2[i+1]-x1[i+1])/((x2[i+1]-x1[i+1])**2+(y2[i+1]-y1[i+1])**2)**1.5 )
ay2.append( G*M*y2[i+1]/(x1[i+1]**2+y1[i+1]**2)**1.5 + G*m1*(y2[i+1]-y1[i+1])/((x2[i+1]-x1[i+1])**2+(y2[i+1]-y1[i+1])**2)**1.5 )
vx1.append( vx1[i] + h*(ax1[i+1] + ax1[i] )/2 )
vy1.append( vy1[i] + h*(ay1[i+1] + ay1[i] )/2 )
vx2.append( vx2[i] + h*(ax2[i+1] + ax2[i] )/2 )
vy2.append( vy2[i] + h*(ay2[i+1] + ay2[i] )/2 )
Etmp = m1*(0.5*(vx1[i]**2 + vy1[i]**2) + G*M/sqrt(x1[i]** 2+ y1[i]**2))
Etmp+= m2*(0.5*(vx2[i]**2 + vy2[i]**2) + G*M/sqrt(x2[i]** 2+ y2[i]**2))
Etmp+= G*m1*m2/sqrt((x1[i]-x2[i])**2+(y1[i]-y2[i])**2)
E.append( Etmp )
e.append( 100*( Etmp - E0 )/E0 )
# Drawing the screen ###################################################
# Close event
for event in pygame.event.get():
if event.type == QUIT:
pygame.quit(); sys.exit();
msElapsed = clock.tick(120)
X1 = int( sizex/2.+sizex/2.*x1[i]/4. )
Y1 = int( sizey/2.-sizey/2.*y1[i]/4. )
X2 = int( sizex/2.+sizex/2.*x2[i]/4. )
Y2 = int( sizey/2.-sizey/2.*y2[i]/4. )
planet1 = pygame.Rect(X1,Y1,sizeqx,sizeqy)
planet2 = pygame.Rect(X2,Y2,sizeqx,sizeqy)
pygame.draw.rect(screen, black, planet1, 0)
pygame.draw.rect(screen, blue , planet2, 0)
pygame.draw.rect(screen, white, score, 0)
error="Erro = %.6f %%" %e[i]
tempo="Tempo = %.3f / %.3f Anos" %(t[i],t[-1])
label1 = myfont.render(error, 1, blue, white)
label2 = myfont.render(tempo, 1, blue, white)
screen.blit(label1, (margin, 550))
screen.blit(label2, (250, 550))
pygame.display.update([planet1,planet2,score])
if e[i] > 100.0: #collide
collide = i
if collide > 0:
label3 = myfont.render(u"Colisão!", 1, red, white)
screen.blit(label3, (200, 200))
pygame.display.update([planet1,planet2,score,gameover])
break
print 'Fim'
while True:
for event in pygame.event.get():
if event.type == QUIT:
pygame.quit(); sys.exit();