The motion of a rigid body in a quadratic potential: an integrable discretization
solv-int
2007-05-23 v1 Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.solv-int/9909009,
title = {The motion of a rigid body in a quadratic potential: an integrable discretization},
author = {Yuri B. Suris},
journal= {arXiv preprint arXiv:solv-int/9909009},
year = {2007}
}
Comments
LaTeX, 15 pp