The motion of a rigid body in a quadratic potential: an integrable discretization
| dc.creator | Suris, Yuri B. | |
| dc.date | 1999-09-14 | |
| dc.date.accessioned | 2026-07-07T06:17:53Z | |
| dc.date.available | 2026-07-07T06:17:53Z | |
| dc.description | 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. | |
| dc.description | LaTeX, 15 pp | |
| dc.identifier | https://arxiv.org/abs/solv-int/9909009 | |
| dc.identifier | http://arxiv.org/abs/solv-int/9909009 | |
| dc.identifier | Intern. Math. Research Notices, 2000, No 12, p.643-663. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94542 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | The motion of a rigid body in a quadratic potential: an integrable discretization | |
| dc.type | text |