Geodesic
Small plane oscillations of satellite in an weakly elliptical orbit
Russian journal of nonlinear dynamics, Tome 9 (2013) no. 4, pp. 671-696.

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

The equation of plane nonlinear oscillations of satellite in an weakly elliptical orbit is investigated. Suppose, that equation of motion contains two small parameters. Various kinds of procedure which reduce the equation to one small parameter case are investigated. Lacks of such procedure are described. New resonance effects of satellite's rotation are described with the help of the generalized averaging method with independent small parameters.
Keywords: independent parameters, average, small oscillations, reductions. 
@article{ND_2013_9_4_a5,
     author = {Pavel S. Krasilnikov},
     title = {Small plane oscillations of satellite in an weakly elliptical orbit},
     journal = {Russian journal of nonlinear dynamics},
     pages = {671--696},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2013_9_4_a5/}
}
TY  - JOUR
AU  - Pavel S. Krasilnikov
TI  - Small plane oscillations of satellite in an weakly elliptical orbit
JO  - Russian journal of nonlinear dynamics
PY  - 2013
SP  - 671
EP  - 696
VL  - 9
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2013_9_4_a5/
LA  - ru
ID  - ND_2013_9_4_a5
ER  - 
%0 Journal Article
%A Pavel S. Krasilnikov
%T Small plane oscillations of satellite in an weakly elliptical orbit
%J Russian journal of nonlinear dynamics
%D 2013
%P 671-696
%V 9
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2013_9_4_a5/
%G ru
%F ND_2013_9_4_a5
Pavel S. Krasilnikov. Small plane oscillations of satellite in an weakly elliptical orbit. Russian journal of nonlinear dynamics, Tome 9 (2013) no. 4, pp. 671-696. http://geodesic.mathdoc.fr/item/ND_2013_9_4_a5/

[1] Laplace P. S., Traité de la Mécanique Céleste, v. 2, Duprat, Paris, 1799, 382 pp.

[2] Tisserand F., Traité de la Mécanique Céleste, v. 2, Théorie de la figure des corps célestes et de leur mouvement de rotation, Gauthier-Villars, Paris, 1891, 552 pp.

[3] Routh E. J., A treatise on the dynamics of a system of rigid bodies, v. 2, The advanced part, 6th ed., Macmillan, New York, 1905 ; Dover, New York, 1955 (reprint) | Zbl | Zbl

[4] Baker R. M. L. Jr., “Passive stability of a satellite vihicle”, Navigation, 6:1 (1958), 64–65

[5] Baker R. M. L. Jr., “Librations on a slightly eccentric orbit”, ARS Journal, 30:1 (1960), 124–126 | Zbl

[6] Klemperer W. B., Baker R. M. L. Jr., “Satellite librations”, Astronaut. Acta, 3:1 (1957), 16–27 | MR

[7] Stocker T. A., Vachino R. F., “The two-dimensional librations of a dumbbell-shaped satellite in a uniform gravitational field”, Proc. of the Western Regional Meeting of the AAS (August, 1958), Advances in Astronaut. Sci., 3, eds. N. V. Peterson, H. Jacobs, American Astronautical Society, New York, 1958, AAS 58-037

[8] Beletskii V. V., “O libratsii sputnika”, Iskusstvennye sputniki Zemli, 3, ed. L. V. Kurnosova, AN SSSR, M., 1959, 13–31 | Zbl

[9] Beletskii V. V., “Libratsiya sputnika na ellipticheskoi orbite”, Iskusstvennye sputniki Zemli, 16, ed. L. V. Kurnosova, AN SSSR, M., 1963, 46–56 | Zbl

[10] Bardin B. S., “O vetvlenii periodicheskikh reshenii sistemy, blizkoi k sisteme Lyapunova”, PMM, 63:4 (1999), 538–548 | MR | Zbl

[11] Bardin B. S., “On nonlinear motions of a Hamiltonian system in the case of external resonance”, Rep. Math. Phys., 49:2–3 (2002), 133–142 | DOI | MR | Zbl

[12] Demin V. G., Singkh R. B., “Nelineinye ploskie kolebaniya sputnika na ellipticheskoi orbite”, Kosmicheskie issledovaniya, 11:2 (1973), 192–197

[13] Schechter H. B., “Dumbbell librations in elliptic orbits”, AIAA Journal, 2:6 (1964), 1000–1003 | DOI | Zbl

[14] Liu F. C., “Periodic solution of plane libration motion of a satellite”, AIAA Journal, 9:7 (1971), 1240–1244 | DOI | Zbl

[15] Sarychev V. A., Voprosy orientatsii iskusstvennykh sputnikov, Itogi nauki i tekhniki. Ser. Issledovanie kosmicheskogo prostranstva, 11, VINITI, M., 1978, 223 pp.

[16] Markeev A. P., “K zadache o ploskikh periodicheskikh vrascheniyakh sputnika na ellipticheskoi orbite”, MTT, 2008, no. 3, 102–115

[17] Sarychev V. A., Sazonov V. V., Zlatoustov V. A., “Periodicheskie vrascheniya sputnika v ploskosti ellipticheskoi orbity”, Kosmicheskie issledovaniya, 17:2 (1979), 190–207

[18] Sarychev V. A., Sazonov V. V., Zlatoustov V. A., “Nesimmetrichnye periodicheskie kolebaniya sputnika v ploskosti ellipticheskoi orbity”, Kosmicheskie issledovaniya, 18:1 (1980), 3–10

[19] Bryuno A. D., “Semeistva periodicheskikh reshenii uravneniya Beletskogo”, Kosmicheskie issledovaniya, 40:3 (2002), 295–316 | MR

[20] Varin V. P., Kriticheskie semeistva periodicheskikh reshenii uravneniya kolebanii sputnika, Preprint No 101, IPM RAN, M., 1996, 30 pp.

[21] Markeev A. P., “Nelineinye kolebaniya sputnika pri rezonanse $1:1:1$”, PMM, 76:1 (2012), 52–68 | MR | Zbl

[22] Krasilnikov P. S., “Metod usredneniya kak protsedura vydeleniya glavnykh chlenov v ryadakh reshenii”, Sbornik nauchno-metodicheskikh statei po teoreticheskoi mekhanike, ed. Yu. G. Martynenko, MGU, M., 2009, 56–68 | MR

[23] Krasilnikov P. S., “O nelineinykh kolebaniyakh mayatnika peremennoi dliny na vibriruyuschem osnovanii”, PMM, 76:1 (2012), 36–51 | MR | Zbl

[24] Beletskii V. V., Dvizhenie sputnika otnositelno tsentra mass v gravitatsionnom pole, MGU, M., 1975, 308 pp.