Abstract
The topology of a new intagrable version of a nonholonomic Suslov problem is considered. It is shown that the integral manifolds are either Liouville tori with quasiperiodic windings or closed two-dimensional surfaces almost all trajectories on which are closed. Bibliography18 titles.
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References
A. T. Fomenko, “Morse theory of integrable Hamiltonian systems”,Dokl. Akad. Nauk SSSR,287, 1072–1075 (1986).
A. T. Fomenko,Integrability and Nonintegrability in Geometry and Mechanics, Kluwer Academic Publishers, Dordrecht (1988).
A. T. Fomenko, “Qualitative geometrical theory of integrable systems. classification of isoenergetic surfaces and bifurcation of Liouville tori at the critical energy values”,Lect. Notes Math.,1334, 221–245 (1988).
A. T. Fomenko, “The theory of invariants of muldimensional integrable Hamiltonian systems (with arbitrary many degrees of freedom). Molecular table of all integrable systems with two degrees of freedom”,Advances in Soviet Math.,6, 1–35 (1991).
A. T. Fomenko, “Theory of rough classification of integrable nondegenerate Hamiltonian differential equations on four-dimensional manifolds. application to classical mechanics”,Advances in Soviet Math.,6 (1991).
G. G. Okuneva, “Integrable Hamiltonian systems in analytic dynamics and mathematical physics”,Advances in Soviet Math.,6, 37–65 (1991).
A. A. Oshemkov, “Fomenko invariants for the main integrable cases of the rigid body motion equations”,Advances in Soviet Math.,6, 67–146 (1991).
Y. Sinagawa, Y. L. Kergosien, and T. L. Kunii, “Surface coding based on Morse theory”,IEEE Computer Graphics and Applications,11, 66–78 (1991).
Y. Shinagawa, T. L. Kunii, A. T. Fomenko, and S. Takahashi,Coding of Object Surfaces Using Atoms, in press: Frontiers in Scientific Visualization (Larry Rosenblum, eds.).
G. K. Suslov.Theoretical Mechanics [in Russian], Gostekhizdat, Moscow (1946).
G. V. Gorr, L. V. Kudryashoba, and L. A. Stepanova,Classical Problems in the Dynamics of a Solid Body [in Russian], Naukova Dumka, Kiev (1978).
G. G. Okuneva, “Movement of a rigid body with fixed point under nonholonomic connection in Newton field”,Mekh. Tverd. Tela, No. 18, 40–43 (1986).
G. G. Okuneva, “Orbital topological classification of flows with closed trajectories”,Continuous Maps of Topological Spaces [in Russian], Izdat. Latv. Univ. (1986), pp. 170–175.
G. G. Okuneva, “Orbital topological classification of two-dimensional flows with almost all trajectories closed. Abstracts, Part 2”,Internat. Topology Conference, Baku, p. 225 (1987).
G. G. Okuneva, “Qualitive investigation of an integrable variant of the nonholonomic Suslov problem”,Vest. MGU, Ser. Mat. Mekh., No. 5, 59–64 (1987).
D. N. Goryachev, “On motion of a rigid body about a fixed point in the caseA=B=4C”,Mat. Sb.,21, No. 3 (1900).
E. V. Anoshkina, “Topological classification of integrable systems in Goryachev-Chaplygin case with generalized potential”,Usp. Mat. Nauk,47, No. 3 (1992).
E. V. Anoshkina, “Topological classification of integrable systems in the case of generalized hyrostat”, Manuscript deposited in VINITI,B293, (1993).
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Published inZapiski Nauchnykh Seminarov POMI, Vol. 235, 1900, pp. 7–21.
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Anoshkina, E.V., Kunii, T.L., Okuneva, G.G. et al. On the topology of an integrable variant of a nonholonomic Suslov problem. J Math Sci 94, 1448–1456 (1999). https://doi.org/10.1007/BF02365196
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DOI: https://doi.org/10.1007/BF02365196