Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2015-5pp.416-425

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V.V. Sazonov and A.V. Troitskaya, "Periodic motions of a gyrostat satellite with a large gyrostatic moment about the centre of mass," J. Appl. Math. Mech. 79 (5), 416-425 (2015)
Year 2015 Volume 79 Issue 5 Pages 416-425
DOI 10.1016/j.jappmathmech.2016.03.001
Title Periodic motions of a gyrostat satellite with a large gyrostatic moment about the centre of mass
Author(s) V.V. Sazonov (M.V. Keldysh Institute of Applied Mathematics, Moscow, Russia, sazonov@keldysh.ru)
A.V. Troitskaya (M.V. Keldysh Institute of Applied Mathematics, Moscow, Russia)
Abstract An axisymmetric gyrostat satellite, whose centre of mass moves in a fixed circular orbit about an attractive centre is considered. The satellite moves about the centre of mass under the action of the gravitational moment. Under the assumption that the gyrostatic moment of the satellite is large and is directed along its axis of symmetry, the periodic motions of this axis are investigated in a small vicinity of a fixed direction, lying in the orbital plane in absolute space. Such motions are described by a system of fourth-order differential equations with periodic coefficients that contains a large parameter. A theorem for the existence and uniqueness of a symmetric periodic solution of this system that has the required properties is proved using methods for constructing periodic solutions of differential equations with a large parameter.
Received 25 November 2014
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