 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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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 |
| Link to Fulltext |
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