A rigid body dynamics derived from a class of extended Gaudin models : an integrable discretization
| dc.creator | Musso, F. | |
| dc.creator | Petrera, M. | |
| dc.creator | Ragnisco, O. | |
| dc.creator | Satta, G. | |
| dc.date | 2005-03-01 | |
| dc.date.accessioned | 2026-07-07T04:31:54Z | |
| dc.date.available | 2026-07-07T04:31:54Z | |
| dc.description | We consider a hierarchy of classical Liouville completely integrable models sharing the same (linear) $r$--matrix structure obtained through an $N$--th jet--extension of $\mathfrak{su}(2)$ rational Gaudin models. The main goal of the present paper is the study of the integrable model corresponding to N=3, since the case N=2 has been considered by the authors in separate papers, both in the one--body case (Lagrange top) and in the $n$--body one (Lagrange chain). We now obtain a rigid body associated with a Lie--Poisson algebra which is an extension of the Lie--Poisson structure for the two--field top, thus breaking its semidirect product structure. In the second part of the paper we construct an integrable discretization of a suitable continuous Hamiltonian flow for the system. The map is constructed following the theory of Bäcklund transformations for finite--dimensional integrable systems developed by V.B. Kuznetsov and E.K. Sklyanin. | |
| dc.description | 15 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math-ph/0503002 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0503002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57993 | |
| dc.subject | Mathematical Physics | |
| dc.title | A rigid body dynamics derived from a class of extended Gaudin models : an integrable discretization | |
| dc.type | text |