Moscow University Mechanics Bulletin

, Volume 71, Issue 2, pp 27–32 | Cite as

Integrable systems in the dynamics on the tangent bundle of a two-dimensional sphere

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Abstract

A mechanical system whose phase space is the tangent bundle of a two-dimensional sphere is studied. The potential nonconservative systems describing a geodesic flow are classified. A multiparameter family of systems possessing a complete set of transcendental first integrals expressed in terms of finite combinations of elementary functions is found. Some examples illustrating the spatial dynamics of a rigid body interacting with a medium are discussed.

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© Allerton Press, Inc. 2016

Authors and Affiliations

  1. 1.Moscow University Institute of Mechanics, Leninskie GoryMoscow State UniversityMoscowRussia

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