Geodesic
On the stability of a resonant rotation of a satellite in an elliptic orbit
Russian journal of nonlinear dynamics, Tome 12 (2016) no. 4, pp. 619-632.

Voir la notice de l'article provenant de la source Math-Net.Ru

We deal with the problem of stability for a resonant rotation of a satellite. It is supposed that the satellite is a rigid body whose center of mass moves in an elliptic orbit. The resonant rotation is a planar motion such that the body completes one rotation in absolute space during two orbital revolutions of its center of mass. The stability analysis of the resonant rotation with respect to planar perturbations has been performed in detail earlier. In this paper we investigate the stability of the resonant rotation with respect to both planar and spatial perturbations for a nonsymmetric satellite. For small values of the eccentricity we have obtained boundaries of instability domains (parametric resonance domains) in an analytic form. For arbitrary eccentricity values we numerically construct domains of stability in linear approximation. Outside the above stability domains the resonant rotation is unstable in the sense of Lyapunov.
Keywords: Hamiltonian system, resonant periodic motion, parametric resonance, stability.
Mots-clés : satellite 
@article{ND_2016_12_4_a5,
     author = {B. S. Bardin and E. A. Chekina},
     title = {On the stability of a resonant rotation of a satellite in an elliptic orbit},
     journal = {Russian journal of nonlinear dynamics},
     pages = {619--632},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2016_12_4_a5/}
}
TY  - JOUR
AU  - B. S. Bardin
AU  - E. A. Chekina
TI  - On the stability of a resonant rotation of a satellite in an elliptic orbit
JO  - Russian journal of nonlinear dynamics
PY  - 2016
SP  - 619
EP  - 632
VL  - 12
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2016_12_4_a5/
LA  - ru
ID  - ND_2016_12_4_a5
ER  - 
%0 Journal Article
%A B. S. Bardin
%A E. A. Chekina
%T On the stability of a resonant rotation of a satellite in an elliptic orbit
%J Russian journal of nonlinear dynamics
%D 2016
%P 619-632
%V 12
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2016_12_4_a5/
%G ru
%F ND_2016_12_4_a5
B. S. Bardin; E. A. Chekina. On the stability of a resonant rotation of a satellite in an elliptic orbit. Russian journal of nonlinear dynamics, Tome 12 (2016) no. 4, pp. 619-632. http://geodesic.mathdoc.fr/item/ND_2016_12_4_a5/

[1] Khentov A. A., “On rotational motion of a satellite”, Kosmicheskie Issledovaniya, 22:1 (1984), 130–131 (Russian)

[2] Markeev A. P., Bardin B. S., “A planar, rotational motion of a satellite in an elliptic orbit”, Cosmic Research, 32:6 (1994), 583–589

[3] Bardin B. S., Chekina E. A., Chekin A. M., “On the stability of a planar resonant rotation of a satellite in an elliptic orbit”, Regul. Chaotic Dyn., 20:1 (2015), 63–73 | DOI | MR | Zbl

[4] Bardin B. S., Chekina E. A., “On stability of a resonant rotation of a symmetric satellite in an elliptic orbit”, Regul. Chaotic Dyn., 21:4 (2016), 377–389 | DOI | MR | Zbl

[5] Markeev A. P., Linear Hamiltonian systems and some problems of stability of the satellite center of mass, R Dynamics, Institute of Computer Science, Izhevsk, 2009 (Russian)

[6] Beletskii, V. V. and Shlyakhtin, A. N., Resonance Rotations of a Satellite with Interactions between Magnetic and Gravitational Fields,, Preprint No 46, Institute of Applied Mathematics, Academy of Sciences of the USSR, Moscow, 1980, 30 pp. (Russian)

[7] Malkin I. G., Theory of stability of motion, Univ. of Michigan, Ann Arbor, Mich., 1958, 456 pp. | MR

[8] Yakubovich V. A., Starzhinskii V. M., Parametric resonance in linear systems, Nauka, Moscow, 1987, 328 pp. (Russian) | MR

[9] Lyapunov A. M., “On stability of motion in a special case of the three-body problem”, Collected Works, v. 1, AN SSSR, Moscow, 1954, 327–401 (Russian)