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IssuesArchive of Issues2007-4pp.507-516

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T. E. Churkina, "Stability of a planar resonance satellite motion under spatial perturbations," Mech. Solids. 42 (4), 507-516 (2007)
Year 2007 Volume 42 Number 4 Pages 507-516
Title Stability of a planar resonance satellite motion under spatial perturbations
Author(s) T. E. Churkina (Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993, Russia, tania@serokhvostov.aviel.ru)
Abstract The satellite motion relative to the center of mass in a central Newtonian gravitational field on an elliptic orbit is considered. The satellite is a rigid body whose linear dimensions are small compared with the orbit dimensions. We study a special case of planar motion in which the satellite rotates in the orbit plane and performs three revolutions in absolute space per two revolutions of the center of mass in the orbit. Perturbations are assumed to be arbitrary (they can be planar as well as spatial). In the parameter space of the problem, we obtain Lyapunov instability domains and domains of stability in the first approximation. In the latter, we construct third- and fourth-order resonance curves and perform nonlinear stability analysis of the motion on these curves. Stability was studied analytically for small eccentricity values and numerically for arbitrary eccentricity values.
References
1.  V. V. Beletskii, Artificial Satellite Motion about Its Center of Mass (Nauka, Moscow, 1965) [in Russian].
2.  V. V. Beletskii and E. K. Lavrovskii, "To the Theory of Mercury Resonance Rotation," Astron. Zh. 52 (6), 1299-1308 (1975).
3.  A. A. Khentov, "On the Stability in the First Approximation of the Earth Artificial Satellite Rotation about the Center of Mass," Kosmich. Issled. 6 (5), 793-795 (1968).
4.  A. P. Markeev, "Stability of Equilibrium States of Hamiltonian Systems: a Method of Investigation," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 3-12 (2004) [Mech. Solids (Engl. Transl.)].
5.  A. P. Markeev, Libration Points in Celestial Mechanics and Space Dynamics (Nauka, Moscow, 1978) [in Russian].
6.  V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients and Their Applications (Nauka, Moscow, 1972) [in Russian].
7.  V. V. Beletskii, Satellite Motion about the Center of Mass in Gravitational Field (Izd-vo MGU, Moscow, 1975) [in Russian].
8.  A. M. Lyapunov, "On Stability of Motion in a Special Case of the Three-Body Problem," in Collected Works (Izd-vo AN SSSR, Moscow-Leningrad, 1954) Vol. 1, pp. 327-401 [in Russian].
9.  A. P. Markeev, "Constructive Algorithm for Normalization of a Periodic Hamiltonian," Prikl. Mat. Mekh. 69 (3), 355-371 (2005) [J. Appl. Math. Mech. (Engl. Transl.)].
10.  J. Mozer, "New Aspects in the Theory of Stability of Hamiltonian Systems," Comm. Pure and Appl. Math. 11 (1), 81-114 (1958).
11.  A. P. Markeev, "Stability of Hamiltonian Systems," in Nonlinear Mechanics (Fizmatgiz, Moscow, 2001), pp. 114-130 [in Russian].
Received 23 January 2007
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