import numpy as np
import matplotlib.pyplot as plt

radius = 2
angularSpeed = .1
angle_ini = np.pi/6
angle_max = 2.3 * 2*np.pi
N_images = 300
T = np.linspace(0, angle_max/angularSpeed, N_images)  # vector: time for each image
L = angle_max*radius


## figure and axes
fig = plt.figure(figsize=(14, 6))
axis = fig.add_subplot(111, aspect='equal', frameon=False)
axis.set_xticks([])
axis.set_yticks([])
# axis.set_xlim(-1, 10), 
axis.set_ylim(-.3, 2*1.1*radius)


## line (along which the movement takes place)
axis.plot([1.2*radius, -L - 1.2*radius], [0, 0], color='k')


## initial circle
Theta = np.linspace(0, 2*np.pi, 300)
x_circle = radius*np.cos(Theta)
y_circle = radius + radius*np.sin(Theta)

circle = axis.plot(x_circle, y_circle, linewidth=.5, color='b')[-1]


## curve (cycloid)
X = radius*np.cos(angle_ini + angularSpeed*T) - angularSpeed*T*radius
Y = radius + radius*np.sin(angle_ini + angularSpeed*T)

axis.plot(X, Y, linewidth=.5, color='r')


## initial point
point = axis.plot(X[0], Y[0], marker='o', ms='3', color=(.6, 0, 0))[-1]


## animation
for n in range(N_images):
    t = T[n]
    # the circle is modified
    circle.set_xdata(x_circle - angularSpeed*t*radius)
    circle.set_ydata(y_circle)

    # the point is modified
    point.set_xdata(X[n])
    point.set_ydata(Y[n])

    # pause in the execution of for (to see the image)
    plt.pause(0.05)

plt.show()