 | | 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, "Stability of the cylindrical precession of a satellite in an elliptic orbit," Mech. Solids. 43 (2), 165-172 (2008) |
| Year |
2008 |
Volume |
43 |
Number |
2 |
Pages |
165-172 |
| DOI |
10.3103/S0025654408020015 |
| Title |
Stability of the cylindrical precession of a satellite in an elliptic orbit |
| Author(s) |
A. P. Markeev (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia, markeev@ipmnet.ru) |
| Abstract |
We study the linear problem on the stability of rotation of a dynamically symmetric satellite about the normal to the plane of the orbit of its center of mass. The orbit is assumed to be elliptic, and the orbit eccentricity is arbitrary. We assume that the Hamiltonian contains a small parameter characterizing the deviation of the satellite central ellipsoid of inertia from the sphere. This is a resonance problem, since if the small parameter is zero, then one of the frequencies of small oscillations of the symmetry axis in a neighborhood of the unperturbed rotation of the satellite about the center of mass is exactly equal to the frequency of the satellite revolution in the orbit. We indicate a countable set of values of the angular velocity of the unperturbed rotation for which the resonance is even double. The stability and instability domains are obtained in the first approximation with respect to the small parameter. |
| References |
| 1. | V. A. Sarychev,
"Asymptotically Stable Time-Stationary Rotations of a Satellites,"
Kosmich. Issled.
3 (5), 667-673 (1965)
[Cosmic Res. (Engl. Transl.)
3, 537-543 (1966)]. |
| 2. | V. V. Beletskii,
Satellite Motion about the Center of Mass in Gravitational Field
(Izd-vo MGU, Moscow, 1975)
[in Russian]. |
| 3. | A. P. Markeev,
"On Rotational Motion of a Dynamically Symmetric Satellite in an Elliptic Orbit,"
Kosmich. Issled.
5 (4), 530-539 (1967)
[Cosmic Res. (Engl. Transl.)]. |
| 4. | A. P. Markeev and T. N. Chekhovskaya,
"On the Stability of a Satellite Cylindrical Precession in an Elliptic Orbit,"
Prikl. Mat. Mekh.
40 (6), 1040-1047 (1976)
[J. Appl. Math. Mech. (Engl. Transl.)
40 (6), 984-991 (1976)]. |
| 5. | G. N. Duboshin,
Celestial Mechanics. Fundamental Problems and Methods
(Fizmatgiz, Moscow, 1963;
Translation Div., Wright-Patterson Air-Force Base, Fairborn, Ohio, 1969). |
| 6. | A. P. Markeev,
Theoretical Mechanics
(SPC. "Regular & Chaotic Dynamics," Izhevsk, 2001)
[in Russian]. |
| 7. | G. E. O. Giacaglia,
Perturbation Methods in Nonlinear Systems
(Springer, New York, 1972; Nauka, Moscow, 1979). |
|
| Received |
26 December 2005 |
| Link to Fulltext |
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