This article is cited in 2 papers

On a disk rolling within a sphere

A. G. Kholmskaya

Laboratory of non-linear dynamics and synergetics, Udmurt State University, Universitetskaya, 1, Izhevsk, 426034

Abstract: The rolling without sliding of a round axisymmetrical disk within a sphere is investigated. It is shown that in the absence of a gravity field the problem is integrable in quadratures and the measure of the set of falling orbits is zero. Stationary motions, their necessary and sufficient conditions for stability have been analysed. The trajectory of a contact point has been found. It also has been proved that in a gravitational field almost for all initial conditions the disk will never fall down on the sphere and stationary motions have been considered.

MSC: 70E15, 70F25

Received: 15.03.1998

Language: English

DOI: 10.1070/RD1998v003n01ABEH000064

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