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

Russian Academy of Sciences
in January 1936
(Translated from 1958)
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IssuesArchive of Issues2008-5pp.509-518

Archive of Issues

Total articles in the database: 1813
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A.P. Markeyev, "Rotations of a near-symmetrical satellite in an elliptical orbit with Mercury-type resonance," J. Appl. Math. Mech. 72 (5), 509-518 (2008)
Year 2008 Volume 72 Issue 5 Pages 509-518
Title Rotations of a near-symmetrical satellite in an elliptical orbit with Mercury-type resonance
Author(s) A.P. Markeyev (Moscow, Russia,
Abstract The motion of a satellite, i.e., a rigid body, about to the centre of mass under the action of the gravitational moments of a central Newtonian gravitational field in an elliptical orbit of arbitrary eccentricity is investigated. It is assumed that the satellite is almost dynamically symmetrical. Plane periodic motions for which the ratio of the average value of the absolute angular velocity of the satellite to the average motion of its centre of mass is equal to 3/2 (Mercury-type resonance) are examined. An analytic solution of the non-linear problem of the existence of such motions and their stability to plane perturbations is given. In the special case in which the central ellipsoid of inertia of the satellite is almost spherical, the stability to spatial perturbations is also examined, but only in a linear approximation.
Received 3 April 2008
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