On bi-hamiltonian geometry of some integrable systems on the sphere with cubic integral of motion
arXiv:0812.0217 · doi:10.1088/1751-8113/42/10/105203
Abstract
We obtain bi-Hamiltonian structure for a family of integrable systems on the sphere S with an additional integral of third order in momenta. These results are applied to the Goryachev system and Goryachev-Chaplygin top for which we give an explicit procedure to find the separated coordinates and the separated relations.
11 pages, LaTeX with AMS fonts, corrected typos