 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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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 |
| Link to Fulltext |
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