Periodic Orbits in a Mechanical System with Strongly Coupled Spin and Orbital Motions

Details Periodic Orbits in a Mechanical System with Strongly Coupled Spin and Orbital Motions Periodic Orbits in a Mechanical System with Strongly Coupled Spin and Orbital Motions

Mar 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996aps..mar.m1806h&link_type=abstract

American Physical Society, Annual March Meeting, March 17-22, 1996, abstract #M18.06

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Scientific paper

An ideal superball bouncing on a rigid surface is an interesting and tractible example of a mechanical system in which 'orbital' and 'spin' angular momenta are strongly coupled. Unlike weakly coupled planetary orbits that are planar, strongly coupled orbits are non-planar and quite complex. In particular, orbits of such a ball inside a sphere, while having a certain symmetry in the long term, seem chaotic in the short term. The nine difference equations that describe the motion are coupled and nonlinear. However, discovery of an expression for the symmetry axis(similar to the angular momentum axis in planetary orbits), and transformation into a system defined by this axis causes three of the equations to decouple from the other six, simplifying the solution. The existence of periodic, but unstable orbits are discussed.

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