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]2 ) > 1.0):

self.x[i],self.y[i] = self.correct('np.sqrt(x2+(y)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.reflect(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 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 reflect(self,x,y,vx,vy):

module = np.sqrt(x2+y2) ### normalization

x = x/module

y = y/module

v = np.sqrt(vx2+vy2)

cos1 = (vxx+vyy)/v

cos2 = (vxy-vyx)/v

vt = -v*cos1

vc = v*cos2

vx_n = vtx+vcy

vy_n = vty-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('Circular stadium - trajectory')

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 < 2*np.pi:

x.append(np.cos(theta))

y.append(np.sin(theta))

theta+= 0.02

plt.plot(x,y,'g.')

A=billiard_circle(0.2,0,1,0.6,11000,0.01)

A.motion_calculate()

A.plot()