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This article is cited in 2 scientific papers (total 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.
Received: 11.02.2009 Accepted: 23.03.2009
Citation:
H. M. Yehia, “Further classification of 2D integrable mechanical systems with quadratic invariants”, Regul. Chaotic Dyn., 14:4-5 (2009), 571–579
Linking options:
https://www.mathnet.ru/eng/rcd1000 https://www.mathnet.ru/eng/rcd/v14/i4/p571
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