005_point_circle.py

# This example is unrelated to the course. It's an experiment to test matplotlib animation features

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation

# Set a and b to control the eccentricity of the ellipse
a = 1
b = 1


# Function to update the animation frames
def update(frame):
    global x, y, vx, vy
    # Update position on the circle
    x = a * np.cos(np.radians(frame))
    y = b * np.sin(np.radians(frame))

    # Update velocity components
    vx = -a * np.sin(np.radians(frame))
    vy = b * np.cos(np.radians(frame))

    # Update the position of the point with a trace
    trace_x.append(x)
    trace_y.append(y)
    trace.set_data(trace_x, trace_y)

    # Update the position of the point
    point.set_data([x], [y])

    # Update the velocity graph with a trace
    vel_trace_x.append(vx)
    vel_trace_y.append(vy)
    vel_trace.set_data(vel_trace_x, vel_trace_y)

    # Update the velocity graph
    vel_point.set_data([vx], [vy])

    # Update the arrows
    arrow_pos.set_UVC(x, y)
    arrow_vel.set_offsets([x, y])
    arrow_vel.set_UVC(vx, vy)

    # Update the red arrow from the center to the red dot in the second graph
    center_arrow.set_UVC(vx, vy)

    return point, trace, vel_point, vel_trace, arrow_pos, arrow_vel, center_arrow


# Initial position on the circle
x, y = 1, 0
# Initial velocity components
vx, vy = 0, 1

axis_limit = np.max([a + 0.5, b + 0.5])

# Set up the figure and axis for the animation
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))
ax1.set_xlim(-axis_limit, axis_limit)
ax1.set_ylim(-axis_limit, axis_limit)
ax1.set_aspect("equal")
ax1.set_title("Position in space")

ax1.set_xlabel("$x$")
ax1.set_ylabel("$y$")
ax1.grid(True)

ax2.set_xlim(-axis_limit, axis_limit)
ax2.set_ylim(-axis_limit, axis_limit)
ax2.set_aspect("equal")
ax2.set_title("Velocity space")

ax2.set_xlabel("$v_x$")
ax2.set_ylabel("$v_y$")
ax2.grid(True)

# Create the point on the circle with a trace
trace_x, trace_y = [x], [y]
(trace,) = ax1.plot(trace_x, trace_y, "b-", alpha=0.3)

(point,) = ax1.plot(x, y, "bo", markersize=4)

# Create the velocity point with a trace
vel_trace_x, vel_trace_y = [vx], [vy]
(vel_trace,) = ax2.plot(vel_trace_x, vel_trace_y, "r-", alpha=0.3)

(vel_point,) = ax2.plot([vx], [vy], "ro", markersize=4)

# Create arrow objects for position and velocity
arrow_pos = ax1.quiver(
    0,
    0,
    x,
    y,
    color="blue",
    angles="xy",
    scale_units="xy",
    scale=1,
    width=0.005,
    headwidth=3,
    headlength=4,
    label="Position",
)
arrow_vel = ax1.quiver(
    x,
    y,
    vx,
    vy,
    color="red",
    angles="xy",
    scale_units="xy",
    scale=1,
    width=0.005,
    headwidth=3,
    headlength=4,
    label="Velocity",
)

# Create a red arrow from the center to the red dot in the second graph
center_arrow = ax2.quiver(
    0,
    0,
    vx,
    vy,
    color="red",
    angles="xy",
    scale_units="xy",
    scale=1,
    width=0.005,
    headwidth=3,
    headlength=4,
    label="Velocity",
)

# Create the animation
animation = FuncAnimation(
    fig, update, frames=np.arange(0, 360, 1), interval=10, blit=True
)

# Add legends
ax1.legend()
ax2.legend()

plt.show()