orbit lines.ipynb

Kernel: Python 3 (system-wide)

import matplotlib.pyplot as plt
import numpy as np
from math import sin, cos

# Radii
r = [1, 5]

# angular velocity
w = [2*np.pi, 1]

# sample rate (number of samples per time = 1)
sample_rate = 20

# time step
d_t = 1 / sample_rate

# angle steps
d_theta = [el * d_t for el in w]

# number of time steps total
num_steps = 140

# angle locations
theta = [[(d_theta[j] * i) % (2 * np.pi) for j in range(2)] for i in range(num_steps)]

# generate lines
lines = [[[r[j] * cos(loc[j]), r[j] * sin(loc[j])] for j in range(2)] for loc in theta]

fig, ax = plt.subplots(figsize=(10,10))
ax.set_aspect('equal')
ax.autoscale()

# draw circles
for i in range(2):
    t = np.linspace(0, 2 * np.pi,500)
    x_1 = r[i] * np.cos(t)
    y_1 = r[i] * np.sin(t)
    ax.plot(x_1,y_1,'k');


# draw lines
for line in lines:
    line = np.array(line).T
    ax.plot(*line, 'b', linewidth=.5)