Analyzing Chaotic Motion in a Computational Double Pendulum

This project explores the principles of chaos through the motion of a double pendulum. The motion of the double pendulum is estimated by numerically integrating its Euler-Lagrange equations of motion using numerical integration methods. The motion is simulated using Python and PyGame. The model allows the users to visually observe sensitivity to initial conditions, a defining characteristic of chaotic motion. The conditions which produce chaos in the double pendulum are investigated using quantitative and qualitative measures of chaos. The results illustrate the chaotic nature of the double pendulum and the qualitative results support the use of the Lyapunov exponent as a quantitative measure of chaos.