Stability in bihamiltonian systems and multidimensional rigid body

Magri, 1978, A simple model of the integrable Hamiltonian equation, Journal of Mathematical Physics, 19, 1156, 10.1063/1.523777 Gel’fand, 1979, Hamiltonian operators and algebraic structures related to them, Functional Analysis and its Applications, 13, 248, 10.1007/BF01078363 Reiman, 1980, A family of Hamiltonian structures, hierarchy of Hamiltonians, and reduction for first-order matrix differential operators, Functional Analysis and its Applications, 14, 146, 10.1007/BF01086570 Arnold, 1998 Bolsinov, 1992, Compatible Poisson brackets on Lie algebras and the completeness of families of functions in involution, Mathematics of the USSR-Izvestiya, 38, 69, 10.1070/IM1992v038n01ABEH002187 Bolsinov, 2009, Bi-Hamiltonian structures and singularities of integrable systems, Regular and Chaotic Dynamics, 14, 431, 10.1134/S1560354709040029 A. Bolsinov, A. Izosimov, Singularities of bi-Hamiltonian systems, 2012. arXiv:1203.3419v1. Arnold, 1978 Mishchenko, 1978, Euler equations on finite-dimensional Lie groups, Mathematics of the USSR-Izvestiya, 12, 371, 10.1070/IM1978v012n02ABEH001859 Gel’fand, 1989, Spectral theory of a pencil of skew-symmetric differential operators of third order on S1, Functional Analysis and its Applications, 23, 85, 10.1007/BF01078776 Bolsinov, 2004 Oshemkov, 1987, The topology of surfaces of constant energy and bifurcation diagrams for integrable cases of the dynamics of a rigid body on so(4), Russian Mathematical Surveys, 42, 241, 10.1070/RM1987v042n06ABEH001508 Fehér, 2003, Stability analysis of some integrable Euler equations for SO(n), Journal of Nonlinear Mathematical Physics, 10, 304, 10.2991/jnmp.2003.10.3.4 A. Spiegler, Stability of generic equilibria of the 2N dimensional free rigid body using the energy-Casimir method, Ph.D. Thesis, University of Arizona, 2006. Birtea, 2012, Stability of equilibria for the so(4) free rigid body, Journal of Nonlinear Science, 22, 187212, 10.1007/s00332-011-9113-2 P. Birtea, I. Caşu, Energy methods in the stability problem for the so(4) free rigid body, 2011. arXiv:1010.0295v2. I. Caşu, On the stability problem for the so(5) free rigid body, 2011. arXiv:1009.2387v2. Manakov, 1976, Note on the integration of Euler’s equations of the dynamics of an n-dimensional rigid body, Functional Analysis and its Applications, 10, 328, 10.1007/BF01076037 Izosimov, 2012, A note on relative equilibria of multidimensional rigid body, Journal of Physics A: Mathematical and Theoretical, 45, 325203, 10.1088/1751-8113/45/32/325203 A. Izosimov, Stability of relative equilibria of multidimensional rigid body, 2012. arXiv:1203.3985v1.