A rigid body dynamics derived from a class of extended Gaudin models : an integrable discretization

dc.creatorMusso, F.
dc.creatorPetrera, M.
dc.creatorRagnisco, O.
dc.creatorSatta, G.
dc.date2005-03-01
dc.date.accessioned2026-07-07T04:31:54Z
dc.date.available2026-07-07T04:31:54Z
dc.descriptionWe 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.description15 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math-ph/0503002
dc.identifierhttp://arxiv.org/abs/math-ph/0503002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57993
dc.subjectMathematical Physics
dc.titleA rigid body dynamics derived from a class of extended Gaudin models : an integrable discretization
dc.typetext

Files

Collections