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Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)
Bicentennial of C.G. Jacobi
A rigid body dynamics derived from a class of extended Gaudin models: an integrable discretization
F. Musso, M. Petrera, O. Ragnisco, G. Satta Dipartimento di Fisica 'E Amaldi',
Universitá degli Studi 'Roma Tre',
Via della Vasca Navale 84, I-00146 Rome, Italy
Аннотация:
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.
Ключевые слова:
models, Bäcklund transformations, spinning tops.
Поступила в редакцию: 22.03.2005 Принята в печать: 04.05.2005
Образец цитирования:
F. Musso, M. Petrera, O. Ragnisco, G. Satta, “A rigid body dynamics derived from a class of extended Gaudin models: an integrable discretization”, Regul. Chaotic Dyn., 10:4 (2005), 363–380
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd715 https://www.mathnet.ru/rus/rcd/v10/i4/p363
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