"""
Created on Wed Nov 16 21:04:04 2016
@author: TanMingjun
"""
import matplotlib.pyplot as plt
import numpy as np
class billiard_circle():
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 (np.sqrt( self.x[i]2+(self.y[i]-0.01)2 ) > 1.0) and self.y[i]>0.01:
self.x[i],self.y[i] = self.correct('np.sqrt(x2+(y-0.01)2) < 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.reflect1(self.x[i],self.y[i],self.vx[i - 1], self.vy[i - 1])
elif (np.sqrt( self.x[i]2+(self.y[i]+0.01)2 ) > 1.0) and self.y[i]<-0.01:
self.x[i],self.y[i] = self.correct('np.sqrt(x2+(y+0.01)2) < 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.reflect2(self.x[i],self.y[i],self.vx[i - 1], self.vy[i - 1])
elif (self.x[i] < -1.0) and self.y[i]>-0.01 and self.y[i]<0.01:
self.x[i],self.y[i] = self.correct('x>-1.0',self.x[i - 1], self.y[i - 1], self.vx[i - 1], self.vy[i - 1])
self.vx[i] = - self.vx[i]
elif (self.x[i] > 1.0) and self.y[i]>-0.01 and self.y[i]<0.01:
self.x[i],self.y[i] = self.correct('x<1.0',self.x[i - 1], self.y[i - 1], self.vx[i - 1], self.vy[i - 1])
self.vx[i] = - self.vx[i]
self.t.append(self.t[i - 1] + self.dt)
return self.x, self.y, self.t
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_cself.dt,y-vy_cself.dt
def reflect1(self,x,y,vx,vy):
module = np.sqrt(x2+(y-0.01)2) ### normalization
x = x/module
y = (y-0.01)/module+0.01
v = np.sqrt(vx2+vy2)
cos1 = (vxx+vy(y-0.01))/v
cos2 = (vx(y-0.01)-vyx)/v
vt = -v*cos1
vc = v*cos2
vx_n = vtx+vc(y-0.01)
vy_n = vt(y-0.01)-vcx
return vx_n,vy_n
def reflect2(self,x,y,vx,vy):
module = np.sqrt(x2+(y+0.01)2) ### normalization
x = x/module
y = (y+0.01)/module-0.01
v = np.sqrt(vx2+vy2)
cos1 = (vxx+vy(y+0.01))/v
cos2 = (vx(y+0.01)-vyx)/v
vt = -v*cos1
vc = v*cos2
vx_n = vtx+vc(y+0.01)
vy_n = vt(y+0.01)-vcx
return vx_n,vy_n
def plot(self):
plt.figure(figsize = (8,8))
plt.xlim(-1,1)
plt.ylim(-1,1)
plt.xlabel('x')
plt.ylabel('y')
plt.title('Stadium billiard $\alpha$=0.01')
self.plot_boundary()
plt.plot(self.x,self.y,'y')
#plt.savefig('chapter3_3.31.png',dpi = 144)
plt.show()
def plot_boundary(self):
theta = 0
x = []
y = []
while theta < np.pi:
x.append(np.cos(theta))
y.append(np.sin(theta)+0.01)
theta+= 0.01
plt.plot(x,y,'g.')
while theta > np.pi and theta< 2*np.pi:
x.append(np.cos(theta))
y.append(np.sin(theta)-0.01)
theta+= 0.01
plt.plot(x,y,'g.')
A1=billiard_circle(0,0,1,0.6,4000,0.01)
x1,y1,t1=A1.motion_calculate()
A2=billiard_circle(0.00001,0,1,0.6,4000,0.01)
x2,y2,t2=A2.motion_calculate()
delta=[]
for i in range(len(x1)):
x1[i]=np.sqrt((x1[i]-x2[i])2+(y1[i]-y2[i])2)
plt.semilogy(t1,x1)
plt.title('Stadium with $\alpha$=0.01 - divergence of two trajectories')
plt.xlabel('time')
plt.ylabel('separation')
