We consider a hierarchy of classical Lionville completely integrable models sharing the same (linear) r-matrix structure obtained through an N-th jet-extension of 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 Backlund transformations for finite-dimensional integrable systems developed by V. B. Kuznetsov and E. K. Sklyanin.

Musso F, Petrera M, Ragnisco O, & Satta G (2005). A rigid body dynamics derived from a class of extended Gaudin models: An integrable discretization RID A-7283-2010. REGULAR & CHAOTIC DYNAMICS, 10(4), 363-380 [10.1070/RD2005v010n04ABEH000320].

A rigid body dynamics derived from a class of extended Gaudin models: An integrable discretization RID A-7283-2010

RAGNISCO, Orlando;
2005

Abstract

We consider a hierarchy of classical Lionville completely integrable models sharing the same (linear) r-matrix structure obtained through an N-th jet-extension of 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 Backlund transformations for finite-dimensional integrable systems developed by V. B. Kuznetsov and E. K. Sklyanin.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/138012
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