Geodesic
Stability of stationary rotations of multidimensional rigid body
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2013), pp. 59-62 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is well known that the rotation of a free three-dimensional rigid body around the long and the short axes of inertia is stable, while the rotation around the middle axis is unstable. We generalize this result to the case of many-dimensional space. 
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A. M. Izosimov. Stability of stationary rotations of multidimensional rigid body. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2013), pp. 59-62. http://geodesic.mathdoc.fr/item/VMUMM_2013_1_a11/

[1] Arnold V.I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1989 | MR

[2] Oshemkov A.A., “Topologiya izoenergeticheskikh poverkhnostei i bifurkatsionnye diagrammy dlya nekotorykh integriruemykh sluchaev dinamiki tverdogo tela na $so(4)$”, Uspekhi matem. nauk, 42:6 (1987), 199–200 | MR

[3] Fehér L., Marshall I., “Stability analysis of some integrable Euler equations for $SO(n)$”, J. Nonlinear Math. Phys., 10:3 (2003), 304–317 | DOI | MR

[4] Spiegler A., Stability of generic equilibria of the $2N$ dimensional free rigid body using the energy-Casimir method, Ph.D. Thesis, University of Arizona, Tucson, 2006 | MR

[5] Caşu I., “On the stability problem for the $so(5)$ free rigid body”, Int. J. Geom. Methods Modern Phys., 8 (2011), 1205–1223 | DOI | MR

[6] Birtea P., Caşu I., Energy methods in the stability problem for the $so(4)$ free rigid body, 2011, arXiv: 1010.0295v2 | MR

[7] Birtea P., Caşu I., Ratiu T., Turhan M., “Stability of equilibria for the $so(4)$ free rigid body”, J. Nonlinear Sci., 22 (2012), 187–212 | DOI | MR

[8] Manakov S.V., “Zamechanie ob integrirovanii uravnenii Eilera dinamiki $n$-mernogo tverdogo tela”, Funkts. anal. i ego pril., 10:4 (1976), 93–94 | MR

[9] Mischenko A.S., Fomenko A.T., “Integrirovanie uravnenii Eilera na poluprostykh algebrakh Li”, Dokl. AN SSSR, 231:3 (1976), 536–538 | MR

[10] Mischenko A.S., Fomenko A.T., “Uravneniya Eilera na konechnomernykh gruppakh Li”, Izv. AN SSSR. Ser. matem., 42:2 (1978), 396–415 | MR

[11] Mischenko A.S., Fomenko A.T., “Integriruemost uravnenii Eilera na poluprostykh algebrakh Li”, Tr. Ceminara po vektornomu i tenzornomu analizu, 19, 1979, 3–94

[12] Trofimov V.V., Fomenko A.T., “Integriruemost po Liuvillyu gamiltonovykh sistem na algebrakh Li”, Uspekhi matem. nauk, 39:2 (1984), 3–56 | MR

[13] Ratiu T., “The motion of the free $n$-dimensional rigid body”, Ind. Univ. Math. J., 29 (1980), 609–629 | DOI | MR

[14] Bolsinov A.V., “Soglasovannye skobki Puassona na algebrakh Li i polnota semeistva funktsii v involyutsii”, Izv. AN SSSR. Ser. matem., 55:1 (1991), 69–89 | MR

[15] Bolsinov A.V., Oshemkov A.A., “Bi-hamiltonian structures and singularities of integrable systems”, Regular and Chaotic Dynamics, 14 (2009), 431–454 | DOI | MR

[16] Frahm F., “Über gewisse differentialgleichungen”, Math. Ann., 8 (1874), 35–44 | DOI