96-57 Rupak Chatterjee and A.D. Jackson

SURFING ARNOLD'S WEB (34K, LaTex) Mar 5, 96

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Abstract. The free motion of a rigid one-dimensional stick colliding elastically within an infinitely massive circular wall is first shown to be equivalent to the three-dimensional motion of a billiard ball within a spiral column and then mapped onto a two-dimensional billiard problem with a rotating billiard wall. Indications that such a system has chaotic orbits and can possess integrable orbits is provided through the use of projected Poincar\'{e} sections. When chaotic and integrable orbits co-exist, the chaotic trajectories appear in the form of Arnold's web. We also consider the limit of a stick of zero length in which the system becomes integrable.

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