×

Separation of variables for a pair of integrable systems on \(\mathrm{so}^*(4)\). (English. Russian original) Zbl 1151.37054

Dokl. Math. 76, No. 3, 839-842 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 417, No. 2, 171-174 (2007).
Introduction: A bi-Hamiltonian structure and separation variables are found for a pair of integrable systems on \(\text{so}^*(4)\) with quadratic Hamiltonians and second integrals of motion that are third- and fourth-degree polynomials.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
70E40 Integrable cases of motion in rigid body dynamics
70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] A. V. Borisov and I. S. Mamaev, Solid Dynamics: Hamiltonian Methods, Integrability, Chaos (RKhD, Izhevsk, 2005).
[2] O. V. Goremykin and A. V. Tsiganov, J. Phys. A 37, 4843–4849 (2004). · Zbl 1056.81036 · doi:10.1088/0305-4470/37/17/013
[3] A. Lichnerowicz, J. Differ. Geom. 12, 253–300 (1977). · Zbl 0405.53024 · doi:10.4310/jdg/1214433987
[4] F. Magri, Ann. Inst. Fourier 55, 2147–2159 (2005). · Zbl 1137.70327 · doi:10.5802/aif.2156
[5] V. V. Sokolov, Dokl. Math. 69, 108–111 (2004) [Dokl. Akad. Nauk 394, 602–605 (2004)].
[6] V. V. Sokolov and T. Wolf, J. Phys. A 39, 1915–1926 (2006). · Zbl 1087.37047 · doi:10.1088/0305-4470/39/8/009
[7] A. V. Tsiganov, Reg. Chaot. Dyn. 7, 331–337 (2002). · Zbl 1019.37037 · doi:10.1070/RD2002v007n03ABEH000215
[8] A. V. Tsiganov, Teor. Mat. Fiz. 151, 26–43 (2007). · doi:10.4213/tmf6009
[9] I. Vaisman, Lectures on the Geometry of Poisson Manifolds (Birkhäuser, Basel, 1993). · Zbl 0810.53019
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.