The Lagrange bitop on so(4) x so(4) and geometry of the Prym varieties
arXiv:math-ph/0201036
Abstract
A four-dimensional integrable rigid-body system is considered and it is shown that it represents two twisted three-dimensional Lagrange tops. A polynomial Lax representation, which doesn't fit neither in Dubrovin's nor in Adler - van Moerbeke's picture is presented. The algebro-geometric integration procedure is based on deep facts from the geometry of the Prym varietiesof double coverings of hypeelliptic curves. The correspondence between all such coverings with Prym varieties splitted as a sum of two varieties of the same dimension and the integrable hierarchy associated to the initial system is established.
arXiv comment25 pages, 31 ref
References in corpus (1)
Cited by in corpus (6)
- Systems of Hess-Appel'rot type
- On the Cases of Kirchhoff and Chaplygin of the Kirchhoff Equations
- Systems of Hess-Appel'rot Type and Zhukovskii Property
- The rigid body dynamics: classical and algebro-geometric integration
- Partial Reductions of Hamiltonian Flows and Hess-Appel'rot Systems on SO(n)
- Elliptic Curves and a New Construction of Integrable Systems