This article is cited in 2 papers

Proceedings of GDIS 2008, Belgrade

Further classification of 2D integrable mechanical systems with quadratic invariants

H. M. Yehia

Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Abstract: Four new integrable classes of mechanical systems on Riemannian 2D manifolds admitting a complementary quadratic invariant are introduced. Those systems have quite rich structure. They involve 11–12 arbitrary parameters that determine the metric of the configuration space and forces with scalar and vector potentials. Interpretations of special versions of them are pointed out as problems of motions of rigid body in a liquid or under action of potential and gyroscopic forces and as motions of a particle on the plane, sphere, ellipsoid, pseudo-sphere and other surfaces.

Keywords: integrable Lagrangian systems, quadratic invariants, time-irreversible systems.

MSC: 70H06, 70E40

Received: 11.02.2009
Accepted: 23.03.2009

Language: English

DOI: 10.1134/S1560354709040121

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