  Mechanics of Solids A Journal of Russian Academy of Sciences   Founded
in January 1966
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A. P. Markeev, "Stability of planar rotations of a satellite in a circular orbit," Mech. Solids. 41 (4), 4663 (2006) 
Year 
2006 
Volume 
41 
Number 
4 
Pages 
4663 
Title 
Stability of planar rotations of a satellite in a circular orbit 
Author(s) 
A. P. Markeev (Moscow) 
Abstract 
We study the stability of planar motions of a satellite relative to the
center of mass in a central Newtonian gravitational field. The satellite is
a rigid body whose geometry of mass corresponds to a plate (C=A+B, where
A, B, and C are the principal central moments of inertia). The orbit
of the center of mass is circular. In the unperturbed motion, one of the
principal central axes of inertia of the satellite is perpendicular to the
orbit plane, and the satellite itself rotates around this axis at an
arbitrary angular velocity. The problem on the stability of this rotation
is solved in the nonlinear setting. To this end, we propose a constructive
algorithm for studying the orbital stability of periodic motions of
autonomous Hamiltonian systems. This algorithm is based on a special
construction method and the subsequent analysis of the symplectic mapping
generated by the equations of perturbed motion on the energy level
corresponding to the unperturbed periodic motion. We perform an analytic
study in the case of a nearly dynamically symmetric satellite. Numerical
analysis is used for arbitrary parameter values (the inertial
characteristic and the angular rotation velocity of the satellite). 
References 
1.  V. V. Beletskii, Artificial Satellite Motion Relative to the Center
of Mass [in Russian], Nauka, Moscow, 1965. 
2.  T. R. Kane and D. J. Shippy,
"Attitude stability of a spinning unsymmetrical satellite in a circular orbit,"
J. Astronaut. Sci., Vol. 10, No. 4, pp. 114119, 1963. 
3.  T. R. Kane, "Attitude stability of Earthpointing satellites,"
AIAA Journal, Vol. 3, No. 4, pp. 726731, 1965. 
4.  L. Meirovitch and F. Wallace,
"Attitude instability regions of a spinning unsymmetrical satellite
in a circular orbit,"
J. Astronaut. Sci., Vol. 14, No. 14, pp. 123133, 1967. 
5.  V. V. Sidorenko and A. I. Neishtadt, "Study of stability of
longperiodic planar motions of a satellite in a circular orbit," Kosmicheskie
Issledovaniya, Vol. 38, No. 3, pp. 307321, 2000. 
6.  A. P. Markeev, "Stability of planar oscillations and rotations of
a satellite in a circular orbit," Kosmicheskie Issledovaniya, Vol. 13, No. 3,
pp. 307321, 1975. 
7.  A. P. Markeev and A. G. Sokolskii, "Studies of stability of planar
periodic motions of a satellite in a circular orbit," Izv. AN SSSR. MTT
[Mechanics of Solids], No. 4, pp. 4657, 1977. 
8.  A. P. Markeev and B. S. Bardin,
"On the stability of planar oscillations and rotations of a satellite in a circular orbit,"
Celest. Mech. and Dynam. Astronomy, Vol. 85, No. 1, pp. 5166, 2003. 
9.  A. P. Markeev,
"An algorithm for normalizing the Hamiltonian system in the problem of orbital stability
of periodic motions,"
PMM [Applied Mathematics and Mechanics], Vol. 66, No. 6, pp. 929938. 
10.  A. M. Lyapunov,
"On stability of motion in a special case of the threebody problem,"
in Collected Works [in Russian], Vol. 1, pp. 327401,
Izdvo AN SSSR, MoscowLeningrad, 1954. 
11.  I. G. Malkin,
Theory of Stability of Motion [in Russian],
Nauka, Moscow, 1966. 
12.  A. P. Markeev, Libration Points in Celestial Mechanics and Space
Dynamics [in Russian], Nauka, Moscow, 1978. 
13.  V. A. Yakubovich and V. M. Starzhinskii,
Parametric Resonance in Linear Systems [in Russian],
Nauka, Moscow, 1987. 
14.  G. E. O. Giacaglia,
Perturbation Methods in Nonlinear Systems,
Springer, Berlin, 1972. 
15.  V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt, Mathematical
Aspects of Classical and Celestial Mechanics, Editorial URSS, Moscow, 2002. 
16.  A. P. Markeev, "To the problem of stability of Lagrangian
solutions of the restricted threebody problem," PMM [Applied Mathematics
and Mechanics], Vol. 37, No. 4, pp. 753757, 1973. 
17.  J. Moser,
"New aspects of stability of Hamiltonian systems,"
Comm. Pure Appl. Math., Vol. 11, No. 1, pp. 81114, 1958. 
18.  A. P. Markeev,
Theoretical Mechanics [in Russian],
NITs Regular and Chaotic Dynamics, Izhevsk, 2001. 
19.  J. Glimm,
"Formal stability of Hamiltonian systems," Comm. Pure Appl. Math.,
Vol. 17, No. 4, pp. 509526, 1964. 
20.  A. M. Zhuravskii,
Reference Book in Elliptic Functions [in Russian],
Iszvo AN SSSR, MoscowLeningrad, 1941. 

Received 
01 October 2004 
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