In [99]:

    

%matplotlib inline  
import random
import matplotlib.pyplot as plt
import numpy as np
import math


    

In [100]:

    

nsteps = 1000
rg = np.array(range(nsteps))
velocity = np.zeros(nsteps)
heading = np.zeros(nsteps)


    

In [123]:

    

velocity[0] = 1.25
heading[0] = 0

change = np.cumsum(np.random.poisson(200, 5))
#change_head = 

for i in range(1,1000):
    velocity[i] = velocity[i-1]
    heading[i] = heading[i-1]

    if i in change:
        velocity[i] += random.choice([-1,1]) * random.uniform(-0.5,0.5)
        heading[i] += random.choice([-1,1]) * random.uniform(-math.pi/8,math.pi/8)
plt.plot(velocity)
plt.plot(heading)


    

    
Out[123]:





[<matplotlib.lines.Line2D at 0x7f08374c60b8>]






    

In [124]:

    

def rect(row):
    r = row[0]
    theta = row[1]
    x = r * math.cos(theta)
    y = r * math.sin(theta)
    return np.array([x,y])

trajectory_polar = np.vstack((velocity,heading)).transpose()
trajectory_cart = np.apply_along_axis(rect, 1, trajectory_polar)
plt.plot(trajectory_cart)


    

    
Out[124]:





[<matplotlib.lines.Line2D at 0x7f0837419940>,
 <matplotlib.lines.Line2D at 0x7f0837419a90>]