Tuesday, October 12, 2010

[lcixherr] Compound pendula

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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