  We investigate a variation of the simple double pendulum in which the two
point masses are replaced by square plates. The double square pendulum exhibits
richer behavior than the simple double pendulum and provides a convenient
demonstration of nonlinear dynamics and chaos. It is also an example of an
asymmetric compound double pendulum, which has not been studied in detail. We
obtain the equilibrium configurations and normal modes of oscillation and
derive the equations of motion, which are solved numerically to produce
Poincar\'{e} sections. We show how the behavior varies from regular motion at
low energies, to chaos at intermediate energies, and back to regular motion at
high energies. We also show that the onset of chaos occurs at a significantly
lower energy than for the simple double pendulum.
