Chaos from simplicity : an introduction to the double pendulum

The fusion of two pendulums give rise to a simple mechanical system that on contrary to its deceptively simple appearances exhibit extremely unpredictable and complex behaviour. The equations of motion for the simple double pendulum are derived, and they are used to generate phase portraits and plots of time-for-first-flip. Lyapunov exponents are also computed and show that the larger the release angle of the pendulum, the more sensitive to initial conditions the system becomes. Damping and forcing are then introduced and a brief investigation into the strange attractor of the double pendulum illustrates its chaotic nature