The Double Pendulum problem involves a pendulum hanging from a pendulum.
Editor: The Double Pendulum problem involves a pendulum hanging from a pendulum. Its easy to make one, but its a pretty ferociously difficult mathematical problem, by most peoples standards.

To even set up the relevant highly non-linear dual differential equations requires the formidable somewhat abstract mathematical machinery of Lagrangian Dynamics and Generalised Co-Ordinates. Surprisingly though, the program to solve these equations numerically using the Improved Euler Method is fairly short and simple (once I ironed out my algebraic errors, which are very easy to make). you can free download Double Pendulum Rev 2.2 now.