Double pendulum simulator.

double_pendulum.py

import math, tkinter, time, sys

g = 9.8
m1 = 1
m2 = 1
l1 = 150
l2 = 150
dt = 0.1
theta1 = math.pi / 2
theta2 = math.pi / 2 #+ 0.02
v_theta1 = 0
v_theta2 = 0

mode = sys.argv[1]

def theta1_2(v_theta1, v_theta2, theta1, theta2, g=9.8, m1=1, m2=1, l1=1, l2=1):
    return (g * (math.sin(theta2) * math.cos(theta1 - theta2) - (m1 + m2) / m2 * math.sin(theta1)) - (l1 * v_theta1**2 * math.cos(theta1 - theta2) + l2 * v_theta2**2) * math.sin(theta1 - theta2)) / (l1 * ((m1 + m2) / m2 - math.cos(theta1 - theta2)**2))

def theta2_2(v_theta1, v_theta2, theta1, theta2, g=9.8, m1=1, m2=1, l1=1, l2=1):
    return (g * (m1 + m2) / m2 * (math.cos(theta1 - theta2) * math.sin(theta1) - math.sin(theta2)) + ((m1 + m2) / m2 * l1 * v_theta1**2 + l2 * math.cos(theta1 - theta2) * v_theta2**2) * math.sin(theta1 - theta2)) / (l2 * ((m1 + m2) / m2 - math.cos(theta1 - theta2)**2))

c0 = tkinter.Canvas(width=640, height=480)
c0.pack()
x1 = 320 + l1 * math.sin(theta1)
y1 = 150 + l1 * math.cos(theta1)
x2 = x1 + l2 * math.sin(theta2)
y2 = y1 + l2 * math.cos(theta2)
c0.create_line(320, 150, x1, y1, tags="bar1", width=3.0)
c0.create_line(x1, y1, x2, y2, tags="bar2", width=3.0)
c0.update()
time.sleep(3)

for i in range(100000):
    a_theta1 = theta1_2(v_theta1, v_theta2, theta1, theta2, g, m1, m2, l1, l2)
    a_theta2 = theta2_2(v_theta1, v_theta2, theta1, theta2, g, m1, m2, l1, l2)
    v_theta1 += a_theta1 * dt
    v_theta2 += a_theta2 * dt
    theta1 += v_theta1 * dt
    theta2 += v_theta2 * dt
    x1 = 320 + l1 * math.sin(theta1)
    y1 = 150 + l1 * math.cos(theta1)
    x2 = x1 + l2 * math.sin(theta2)
    y2 = y1 + l2 * math.cos(theta2)
    if mode == "trajectory" and i > 0:
        c0.create_line(x0, y0, x2, y2, fill="red", smooth=True, tags="tj")
    c0.coords("bar1", 320, 150, x1, y1)
    c0.coords("bar2", x1, y1, x2, y2)
    x0 = x2
    y0 = y2
    time.sleep(dt*0.1)
    c0.update()
tkinter.mainloop()