Python Coding

Next project:

If a ray is reflected inside a rectangular box (whose inside is mirror) and if the ray falls on a side and get reflected, it will come back to the starting point after finite number of reflections if the slipe of y=mx+c ray , m=rational number. If m is irrational, then the ray will never come back to the original starting point and the whole box will light up i.e., it will fill the box inside.

I shall do it by using c/c++ or Python or Mathematica and show the result here in future.

Animation To show the path of Moon around the Sun. Its not helical as I thought on pen and paper. Its a simply connected single loop, not a perfect circle, not an ellipse, but a closed curve.

I think if irrational numbers are involved in periodicity, it will never come to the same spot again.

I am running all my python code in various methods because i am using Windows, Ubuntu and MacOS

In Ubuntu and MacOS its by creating a virtual environment

In Windows, I am doing it by IDLE.

import numpy as npimport matplotlib.pyplot as pltfrom matplotlib.animation import FuncAnimation
# ParametersR = 2.0 # Red bead orbit radiusd = 0.1 # Blue bead distance from red beadr_g = 0.5 # Green bead orbit radius around red bead
omega_main = 1.0 # Main rotation frequencyomega_orbit = 2.0 # Green bead's own rotation frequency
dt = 0.05
# Lists to store trajectory pointstrail_red_x, trail_red_y = [], []trail_blue_x, trail_blue_y = [], []trail_green_x, trail_green_y = [], []
# Figurefig, ax = plt.subplots()ax.set_aspect('equal')ax.set_xlim(-3, 3)ax.set_ylim(-3, 3)
# Orbital reference circletheta = np.linspace(0, 2*np.pi, 300)ax.plot(R*np.cos(theta), R*np.sin(theta), 'k--')
# Beadsred_bead, = ax.plot([], [], 'ro', markersize=12)blue_bead, = ax.plot([], [], 'bo', markersize=8)green_bead, = ax.plot([], [], 'go', markersize=10)
# Connecting rodsrod_rb, = ax.plot([], [], 'gray', linewidth=2)rod_rg, = ax.plot([], [], 'gray', linewidth=2)
# Trails (grey lines)trail_red_line, = ax.plot([], [], color='gray', linewidth=0.5)trail_blue_line, = ax.plot([], [], color='gray', linewidth=1)trail_green_line, = ax.plot([], [], color='green', linewidth=3)

def update(frame):    t = frame * dt
    # --- Main bead rotation ---    angle = omega_main * t
    # Red bead position    x_r = R * np.cos(angle)    y_r = R * np.sin(angle)
    # Blue bead (rigid link)    x_b = x_r + d * np.cos(angle)    y_b = y_r + d * np.sin(angle)
    # Green bead (rotating around red)    phi = omega_orbit * t    x_g = x_r + r_g * np.cos(phi)    y_g = y_r + r_g * np.sin(phi)
    # Update positions    red_bead.set_data([x_r], [y_r])    blue_bead.set_data([x_b], [y_b])    green_bead.set_data([x_g], [y_g])        # Update rods    rod_rb.set_data([x_r, x_b], [y_r, y_b])    rod_rg.set_data([x_r, x_g], [y_r, y_g])
    # Add trail points    trail_red_x.append(x_r); trail_red_y.append(y_r)    trail_blue_x.append(x_b); trail_blue_y.append(y_b)    trail_green_x.append(x_g); trail_green_y.append(y_g)
    # Update trail lines    trail_red_line.set_data(trail_red_x, trail_red_y)    trail_blue_line.set_data(trail_blue_x, trail_blue_y)    trail_green_line.set_data(trail_green_x, trail_green_y)
    return red_bead, blue_bead, green_bead, rod_rb, rod_rg, trail_red_line, trail_blue_line, trail_green_line

ani = FuncAnimation(fig, update, frames=1000, interval=30, blit=True)
plt.title("Three Beads with Motion Trails")plt.show()

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