The Polhode Rolls without Slipping on the Herpolhode Lying in the Invariable Plane

The motion of a rigid body upon which no external forces (or torques) act is a standard problem in intermediate classical mechanics.

I have developed a Maple program which generates an object with three unequal principal moments of inertia, and shows the body, its inertia ellipsoid, the polhode and the herpolhode and the invariable plane.

A terse explanation of the physics and an MPEG movie of one example are also available. You can also see the herpolhode and a projection of the polhode. This example is for a body started rotating very close to the intermediate principal axis


This project was begun at the "Revitalizing the Engineering, Mathematics and Science Curricula via Symbolic Algebra" NSF workshop held at Rose-Hulman Institute of Technology in July 1995. (Homepage) A number of people there were extremely helpful in getting me through the Maple intricacies, including Blair Madore, Bill Farr, Brian Evans, but in particular I want to thank Doug Meade. I also want to thank the organizers of the workshop, Robert J. Lopez and Mark A. Yoder.

Written by Joel A. Shapiro, 1995
This page and the links concerned with rigid body motion may be freely copied and distributed, as long as this notice is included.
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