The motion of a rigid body in a quadratic potential: an integrable discretization

dc.creatorSuris, Yuri B.
dc.date1999-09-14
dc.date.accessioned2026-07-07T06:17:53Z
dc.date.available2026-07-07T06:17:53Z
dc.descriptionThe motion of a rigid body in a quadratic potential is an important example of an integrable Hamiltonian system on a dual to a semidirect product Lie algebra so(n) x Symm(n). We give a Lagrangian derivation of the corresponding equations of motion, and introduce a discrete time analog of this system. The construction is based on the discrete time Lagrangian mechanics on Lie groups, accompanied with the discrete time Lagrangian reduction. The resulting multi-valued map (correspondence) on the dual to so(n) x Symm(n) is Poisson with respect to the Lie-Poisson bracket, and is also completely integrable. We find a Lax representation based on matrix factorisations, in the spirit of Veselov-Moser.
dc.descriptionLaTeX, 15 pp
dc.identifierhttps://arxiv.org/abs/solv-int/9909009
dc.identifierhttp://arxiv.org/abs/solv-int/9909009
dc.identifierIntern. Math. Research Notices, 2000, No 12, p.643-663.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94542
dc.subjectExactly Solvable and Integrable Systems
dc.titleThe motion of a rigid body in a quadratic potential: an integrable discretization
dc.typetext

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