| | 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: | | 12854 |
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In English (Mech. Solids): | | 4810 |
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L. D. Akulenko, D. D. Leshchenko, and A. L. Rachinskaya, "Evolution of the satellite fast rotation due to the gravitational torque in a dragging medium," Mech. Solids. 43 (2), 173-184 (2008) |
Year |
2008 |
Volume |
43 |
Number |
2 |
Pages |
173-184 |
DOI |
10.3103/S0025654408020027 |
Title |
Evolution of the satellite fast rotation due to the gravitational torque in a dragging medium |
Author(s) |
L. D. Akulenko (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia, bolotnik@ipmnet.ru)
D. D. Leshchenko (Odessa State Academy of Civil Engineering and Architecture, Didrikhsona 4, Odessa, 65029, Ukraine, leshchenko_d@ukr.net)
A. L. Rachinskaya (Odessa State Academy of Civil Engineering and Architecture, Didrikhsona 4, Odessa, 65029, Ukraine, rachinskaya@onu.edu.ua) |
Abstract |
We study the fast rotational motion of a dynamically nonsymmetric satellite about the center of mass under the action of the gravitational torque and the drag torque. Orbital motions with arbitrary eccentricity are assumed to be given. The drag torque is assumed to be a linear function of the angular velocity. The system obtained after the averaging over the Euler-Poinsot motion is studied. We discover the following phenomena: the modulus of the angular momentum and the kinetic energy decrease, and there exist quasistationary regimes of motion (along the polhodes). The orientation of the angular momentum vector in the orbital frame of reference is determined. The general case is studied numerically, and an analytic study is performed in a neighborhood of the axial rotation and in the case of small dissipation. |
References |
1. | V. V. Beletskii,
Artificial Satellite Motion about Its Center of Mass
(Nauka, Moscow, 1965)
[in Russian]. |
2. | F. L. Chernous'ko, "On the Motion of a Satellite about Its Center
of Mass under the Action of Gravitational Torques," Prikl. Mat.
Mekh. 27 (3), 474-483 (1963) [J. Appl. Math. Mech. (Engl.
Transl.) 27 (3), 708-722 (1963)]. |
3. | V. V. Beletskii,
Satellite Motion about the Center of Mass in Gravitational Field
(Izd-vo MGU, Moscow, 1975)
[in Russian]. |
4. | V. V. Beletskii and A. M. Yanshin, Aerodynamic Force
Effects on the Rotational Motion of Artificial Satellites (Naukova
Dumka, Kiev, 1984) [in Russian]. |
5. | V. V. Beletskii and A. V. Grushevskii,
"The Evolution of the Rotational Motion of
a Satellite under the Action of a Dissipative Aerodynamic Moment,"
Prikl. Mat. Mekh.
58 (1), 13-20 (1994)
[J. Appl. Math. Mech. (Engl. Transl.)
58 (1), 11-19 (1994)]. |
6. | L. D. Akulenko, D. D. Leshchenko, and F. L. Chernous'ko, "The
Rapid Motion of a Heavy Rigid Body about a Fixed Point in a
Dragging Medium," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 3,
5-13 (1982) [Mech. Solids (Engl. Transl.)]. |
7. | Yu. A. Pupyshev, "The Effect of Gravitational and Aerodynamic
Perturbations on the Rotational Motion around the Center of Mass of
an Asymmetrical Solid Body," Vestnik Leningrad. Univ. Mat. Mekh.
Astronom., No. 7 (2), 129-134 (1971) [Vestnik Leningrad Univ.
Math. (Engl. Transl.)]. |
8. | E. Yu. Kuznetsova, V. V. Sazonov, and S. Yu. Chebukov, "Evolution
of the Satellite Rapid Rotation under the Action of Gravitational
and Aerodynamic Torques," Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 3-14 (2000) [Mech. Solids (Engl. Transl.) 35 (2),
1-10 (2000)]. |
9. | V. M. Volosov and B. I. Morgunov, Averaging Method in the
Theory of Nonlinear Oscillatory Systems (Izd-vo MGU,
Moscow, 1971) [in Russian]. |
10. | L. D. Landau and E. M. Lifshitz,
Course of Theoretical Physics, Vol. 1,
Mechanics
(Nauka, Moscow, 1973; Pergamon Press, Oxford, 1976). |
11. | I. S. Gradshtein and I. M. Ryzhik,
Tables of Integrals, Sums, Series, and Products
(Nauka, Moscow, 1971)
[in Russian]. |
12. | F. L. Chernous'ko,
"Motion of a Rigid Body with Cavities Filled with Viscous Fluid at small Reynolds Numbers,"
Zh. Vychisl. Mat. Mat. Fiz.
5 (6), 1049-1070 (1965)
[U.S.S.R. Comput. Math. Math. Phys. (Engl. Transl.)
5 (6), 99-127 (1965)]. |
13. | E. P. Smirnova,
"Stabilization of Free Rotation of an Asymmetric
Top with Cavities Completely Filled with a Liquid,"
Prikl. Mat. Mekh.
38 (6), 980-985 (1974)
[J. Appl. Math. Mech. (Engl. Transl.)
38 (6), 931-935 (1974)]. |
14. | L. D. Akulenko,
"Higher-Order Averaging Schemes in Systems with Fast and Slow Phases,"
Prikl. Mat. Mekh.
66 (2), 165-176 (2002)
[J. Appl. Math. Mech. (Engl. Transl.)
66 (2), 153-163 (2002)]. |
15. | V. V. Rumiantsev, "On Asymptotic Stability and Instability of
Motion with Respect to a Part of the Variables,"
Prikl. Mat. Mekh.
35 (1), 138-143 (1971)
[J. Appl. Math. Mech. (Engl. Transl.)
35 (1), 105-110 (1971)]. |
|
Received |
08 January 2006 |
Link to Fulltext |
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