Create a display showing a simulated frictionless double pendulum, constantly in motion, never repeating itself. Obey conservation of energy. (And other conservation?) This should be easy. Verlet integration.
A double pendulum will never escape the plane within which it started, but a triple pendulum will. (Update: double pendulum can if ball and socket.) Create 3D display or simulated demonstration of a "forever" triple pendulum.
One possible depiction is a spherical display. The end of the pendulum is projected on a sphere, and brightness represents distance from the center.
Compound pendulums exhibit complicated motion. What happens in the limiting continuous case of a perfectly flexible rope?
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