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IssuesArchive of Issues2015-6pp.603-614

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A.P. Markeev, "Dynamics of a Satellite Carrying a Point Mass Moving about It," Mech. Solids. 50 (6), 603-614 (2015)
Year 2015 Volume 50 Number 6 Pages 603-614
DOI 10.3103/S0025654415060011
Title Dynamics of a Satellite Carrying a Point Mass Moving about It
Author(s) A.P. Markeev (A. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, markeev@ipmnet.ru)
Abstract We study the dynamics of a complex system consisting of a solid and a mass point moving according to a prescribed law along a curve rigidly fixed to the body. The motion occurs in a central Newtonian gravitational field. It is assumed that the orbit of the system center of mass is an ellipse of arbitrary eccentricity.

We obtain equations that describe the motion of the carrier (satellite) about its center of mass. In the case of a circular orbit, we present conditions that should be imposed on the law of the relative motion of the mass point carried by the satellite so that the latter preserves a constant attitude with respect to the orbital coordinate system. In the case of a dynamically symmetric satellite, we consider the problem of existence of stationary and nearly stationary rotations for the case in which the carried point moves along the satellite symmetry axis. We consider several problems of dynamics of the satellite plane motion about its center of mass in an elliptic orbit of arbitrary eccentricity. In particular, we present the law of motion of the carried point in the case without eccentricity oscillations and study the stability of the satellite permanent attitude with respect to the orbital coordinate system.
Keywords system of solids, equilibrium, stability, oscillations
References
1.  R. E. Roberson, "Torques on a Satellite Vehicle from Internal Moving Parts," J. Appl. Mech. 25 (2), 196-200 (1958).
2.  V. S. Aslanov and S. P. Bezglasnyi, "Gravitational Stabilization of a Satellite Using a Movable Mass," Prikl. Mat. Mekh. 76 (4), 563-573 (2012) [J. Appl. Math. Mech. (Engl. Transl.) 76 (4), 405-412 (2012)].
3.  V. V. Beletskii, Satellite Motion about the Center of Mass in Gravitational Field (Izdat. MGU, Moscow, 1975) [in Russian].
4.  A. P. Markeev, Theoretical Mechanics (NITs "Regular and Chaotic Dynamics," Moscow-Izhevsk, 2007) [in Russian].
5.  V. V. Beletskii, Artificial Satellite Motion about Center of Mass (Nauka, Moscow, 1965) [in Russian].
6.  G. N. Duboshin, Celestial Mechanics. Fundamental Problems and Methods (Fizmatgiz, Moscow, 1963) [in Russian].
7.  P. W. Likins, "Stability of Symmetrical Satellite in Attitude Fixed in an Orbiting Reference Frame," J. Astronaut. Sci. 12 (1), 18-24 (1965).
8.  V. A. Sarychev, Problems of Artificial Satellite Orientation, in Progress in Science and Technology, Ser. Study of Cosmic Space, Vol. 11 (VINITI, Moscow, 1978) [in Russian].
9.  A. P. Markeev, Linear Hamiltonian Systems and Some Problems of Satellite Motion Stability about the Center of Mass (NITs "Regular and Chaotic Dynamics," Moscow-Izhevsk, 2009) [in Russian].
10.  I. G. Malkin, Some Problems of the Theory of Nonlinear Vibrations (Gostekhizdat, Moscow, 1956) [in Russian].
Received 02 June 2014
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