dorsal/arxiv
View SchemaThe motion of a rigid body in a quadratic potential: an integrable discretization
| Authors | Yuri B. Suris |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9909009 |
| URL | https://arxiv.org/abs/solv-int/9909009 |
| Journal | Intern. Math. Research Notices, 2000, No 12, p.643-663. |
Abstract
The 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.
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"abstract": "The motion of a rigid body in a quadratic potential is an important example\nof an integrable Hamiltonian system on a dual to a semidirect product Lie\nalgebra so(n) x Symm(n). We give a Lagrangian derivation of the corresponding\nequations of motion, and introduce a discrete time analog of this system. The\nconstruction is based on the discrete time Lagrangian mechanics on Lie groups,\naccompanied with the discrete time Lagrangian reduction. The resulting\nmulti-valued map (correspondence) on the dual to so(n) x Symm(n) is Poisson\nwith respect to the Lie-Poisson bracket, and is also completely integrable. We\nfind a Lax representation based on matrix factorisations, in the spirit of\nVeselov-Moser.",
"arxiv_id": "solv-int/9909009",
"authors": [
"Yuri B. Suris"
],
"categories": [
"solv-int",
"nlin.SI"
],
"journal_ref": "Intern. Math. Research Notices, 2000, No 12, p.643-663.",
"title": "The motion of a rigid body in a quadratic potential: an integrable discretization",
"url": "https://arxiv.org/abs/solv-int/9909009"
},
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