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ellipse and phase.py
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ellipse and phase.py
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# -*- coding: utf-8 -*-
"""
Created on Wed Nov 16 17:29:32 2016
@author: TanMingjun
"""
import matplotlib.pyplot as plt
import numpy as np
class billiard_ellipse:### x^2/3+y^2/2 = 1
def __init__(self,x_0,y_0,vx_0,vy_0,N,dt):
self.x_0 = x_0
self.y_0 = y_0
self.vx_0 = vx_0
self.vy_0 = vy_0
self.N = N
self.dt = dt
def motion_calculate(self):
self.x = []
self.y = []
self.vx = []
self.vy = []
self.t = [0]
self.x.append(self.x_0)
self.y.append(self.y_0)
self.vx.append(self.vx_0)
self.vy.append(self.vy_0)
for i in range(1,self.N):
self.x.append(self.x[i - 1] + self.vx[i - 1]*self.dt)
self.y.append(self.y[i - 1] + self.vy[i - 1]*self.dt)
self.vx.append(self.vx[i - 1])
self.vy.append(self.vy[i - 1])
if (self.x[i]**2/4+self.y[i]**2/3 > 1.0):
self.x[i],self.y[i] = self.correct('x**2/4+y**2/3 < 1.0',self.x[i - 1], self.y[i - 1], self.vx[i - 1], self.vy[i - 1])
self.vx[i],self.vy[i] = self.reflect((3./4)*self.x[i],self.y[i],self.vx[i - 1], self.vy[i - 1])
self.t.append(self.t[i - 1] + self.dt)
return self.x, self.y
def plot(self):
plt.figure(figsize = (8,6))
plt.xlim(-2,2)
plt.ylim(-1.5,1.5)
plt.xlabel('x')
plt.ylabel('y')
self.plot_boundary()
plt.plot(self.x,self.y)
plt.savefig('chapter3_3.31.png',dpi = 144)
plt.show()
def correct(self,condition,x,y,vx,vy):
vx_c = vx/100.0
vy_c = vy/100.0
while eval(condition):
x = x + vx_c*self.dt
y = y + vy_c*self.dt
return x-vx_c*self.dt,y-vy_c*self.dt
def reflect(self,x,y,vx,vy):
module = np.sqrt(x**2+y**2) ### normalization
x = x/module
y = y/module
v = np.sqrt(vx**2+vy**2)
cos1 = (vx*x+vy*y)/v
cos2 = (vx*y-vy*x)/v
vt = -v*cos1
vc = v*cos2
vx_n = vt*x+vc*y
vy_n = vt*y-vc*x
return vx_n,vy_n
# def plot_boundary(self):
# theta = 0
# x = []
# y = []
# while theta < 2*np.pi:
# x.append(np.sqrt(4)*np.cos(theta))
# y.append(np.sqrt(3)*np.sin(theta))
# theta+= 0.01
# plt.title(r'Elliptical stadium $\frac{x^2}{4}+\frac{y^2}{3} = 1$')
# plt.plot(x,y)
def phase_plot(self):
record_x = []
record_vx = []
for i in range(len(self.x)):
if (abs(self.y[i] - 0)<0.001):
record_vx.append(self.vx[i])
record_x.append(self.x[i])
plt.xlabel('x')
plt.ylabel(r'$v_x$')
plt.plot(record_x,record_vx,'.')
#plt.savefig('chapter3_3.31_phasey=0.png', dpi= 144)
plt.show()
A1=billiard_ellipse(2,0,1,0.5,500000,0.01)
A1.motion_calculate()
A1.phase_plot()
A2=billiard_ellipse(0,0,1,0.5,500000,0.01)
A2.motion_calculate()
A2.phase_plot()