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IssuesArchive of Issues2005-1pp.14-25

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A. P. Markeev, "Motion of a rigid body with a single fixed point in the Steklov case," Mech. Solids. 40 (1), 14-25 (2005)
Year 2005 Volume 40 Number 1 Pages 14-25
Title Motion of a rigid body with a single fixed point in the Steklov case
Author(s) A. P. Markeev (Moscow)
Abstract A motion of a heavy rigid body with a single fixed point is analyzed. The center of gravity of the body is located on the medium or the smallest axis of the ellipsoid of inertia. In addition to the "triangle" inequalities usual for a rigid body, the moments of inertia satisfy the conditions B>A>2C or 2B>A>B>C and A>2C. Under these conditions, the Euler-Poisson equations may have particular periodic solutions indicated by V. A. Steklov. In this paper, we study the problem of orbital stability of periodic motions of a rigid body which correspond to the Steklov solutions.
References
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15.  A. P. Markeev, "Algorithm of normalization of the Hamiltonian system for the problem of the orbital stability of periodic motions," PMM [Applied Mathematics and Mechanics], Vol. 66, No. 6, pp. 929-9938, 2002.
16.  V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics [in Russian], Editorial URSS, Moscow, 2002.
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21.  A. P. Markeev, "One approach to the stability abalysis of equilibrium states of Hamiltonian systems," Izv. AN. MTT [Mechanics of Solids], No. 6, pp. 3-12, 2004.
22.  A. P. Markeev, "On area preserving mappings and their applications to the dynamics of systems with collisions," Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 37-54, 1996.
Received 26 April 2004
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