Abstract
We investigated periodic motions of the axis of symmetry of a model satellite of the Earth, which are similar to the motions of the longitudinal axes of the Mir orbital station in 1999–2001 and the Foton-M3 satellite in 2007. The motions of these spacecraft represented weakly disturbed regular Euler precession with the angular momentum vector of motion relative to the center of mass close to the orbital plane. The direction of this vector during the motion was not practically changed. The model satellite represents an axisymmetric gyrostat with gyrostatic moment directed along the axis of symmetry. The satellite moves in a circular orbit and undergoes the action of the gravitational torque. The motion of the axis of symmetry of this satellite relative to the absolute space is described by fourth-order differential equations with periodic coefficients. The periodic solutions to this system with special symmetry properties are constructed using analytical and numerical methods.
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References
Babkin, E.V., Belyaev, M.Yu., Efimov, N.I., et al., Uncontrollable Rotational Motion of the Mir Orbital Station, Kosm. Issled., 2001, vol. 39, no. 1, pp. 27–42. [Cosmic Research, pp. 23–37.]
Babkin, E.V., Belyaev, M.Yu., Efimov, N.I., et al., Uncontrolled Attitude Motion of the Orbital Station Mir in the Last Months of Its Flight, Kosm. Issled., 2003, vol. 41, no. 3, pp. 285–294. [Cosmic Research, pp. 264–273.]
Beuselinck, T., Van Bavinchove, C., Abrashkin, V.I., et al., Determination of Attitude Motion of the Foton M-3 Satellite according to the Data of Onboard Measurements of the Earth’s Magnetic Field, Kosm. Issled., 2010, vol. 48, no. 3, pp. 246–259. [Cosmic Research, pp. 252–265.]
Beuselinck, T., Van Bavinchove, C., Abrashkin, V.I., et al., Determination of Attitude Motion of the Foton M-3 Satellite according to the Data of Onboard Measurements of the Earth’s Magnetic Field, Preprint of Keldysh Inst. of Applied Math., Russ. Acad. Sci., Moscow, 2008, no. 80.
Malkin, I.G., Nekotorye zadachi teorii nelineinykh kolebanii (Some Problems of Theory of Nonlinear Oscillations), Moscow: GITTL, 1956.
Holder, E., Mathematische Untersuchungen zur Himmelsmechanik, Math. Zeitschr., 1929, vol. 31, pp. 197–257.
Lewis, D.C., On the Role of First Integrals in the Perturbation of Periodic Solutions, Ann. Math., 1956, vol. 63, pp. 535–548.
Hale, J.K., Ordinary Differential Equations, New-York: Wiley-Interscience, 1969.
Sarychev, V.A., Sazonov, V.V., and Mel’nik, N.V., Spatial Periodic Oscillations of a Satellite about Its Center of Mass, Kosm. Issled., 1980, vol. 18, no. 5, pp. 659–677. [Cosmic Research, p. 471.]
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Original Russian Text © V.V. Sazonov, 2013, published in Kosmicheskie Issledovaniya, 2013, Vol. 51, No. 2, pp. 145–158.
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Sazonov, V.V. Periodic motions of a satellite-gyrostat relative to its center of mass under the action of gravitational torque. Cosmic Res 51, 133–146 (2013). https://doi.org/10.1134/S0010952513020044
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DOI: https://doi.org/10.1134/S0010952513020044