  Mechanics of Solids A Journal of Russian Academy of Sciences   Founded
in January 1966
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I. A. Neishtadt and V. V. Sazonov, "Periodic oscillations of the axis of symmetry of a satellite under the action of gravitational and aerodynamic torques in a circular orbit," Mech. Solids. 38 (4), 114 (2003) 
Year 
2003 
Volume 
38 
Number 
4 
Pages 
114 
Title 
Periodic oscillations of the axis of symmetry of a satellite under the action of gravitational and aerodynamic torques in a circular orbit 
Author(s) 
I. A. Neishtadt (Moscow)
V. V. Sazonov (Moscow) 
Abstract 
The motion of the symmetry axis of a dynamically symmetric satellite relative to the orbital reference frame under the action of the gravitational torque and the aerodynamic restoring torque is governed by a fourthorder system of differential equations. If the orbit is circular and constant and the density of the aerodynamic flow incident on the satellite is constant, then this system is autonomous and has a generalized energy integral and three families of steadystate solutions. We have investigated periodic solutions of this system, which are close to the steadystate solutions and correspond to rotations of the satellite about the axis of symmetry directed along the normal to the orbital plane. If the magnitude of the projection of the angular velocity of the satellite onto the axis of its symmetry is large, there exist two basic types of such solutions with substantially different periods. Shortperiod solutions describe the satellite motions close to Euler's regular precession. Longperiod solutions correspond to motions that are close to steady rotations about the axis of symmetry, which is slowly moving in the absolute space. For some values of the parameters of the problem, the existence of solutions of both types has been established analytically. By means of numerical calculations, these solutions have been extended to the region of arbitrary values of the parameters. The orbital stability of the obtained solutions has been investigated in the first approximation. Some of the results have been utilized for describing a steady mode of uncontrolled rotation of the satellite "Photon12". 
References 
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[Russian translation], Mir, Moscow, 1966. 
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Some Problems of the Theory of Nonlinear Oscillations [in Russian],
Gostekhizdat, Moscow, 1956. 
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Periodic Solutions of Neartimeinvariant
Systems of Ordinary Differential Equations. Preprint No. 90 [in Russian],
Int Prikl. Mat. AN SSSR, Moscow, 1997. 
5.  V. A. Sarychev, V. V. Sazonov, and N. V. Mel'nik,
"Spatial periodic oscillations of a satellite about the center of mass," Kosmicheskie Issledovaniya, Vol. 18,
No. 5, pp. 659677, 1980. 
6.  V. V. Sazonov, S. Yu. Chebukov, V. I. Abrashkin, A. E. Kazakova,
and A. S. Zaitsev, "Analysis of lowfrequency microaccelerations on board of the satellite Photon11,"
Kosmicheskie Issledovaniya, Vol. 39,
No. 4, pp. 419435, 2001. 
7.  V. I. Abrashkin, V. L. Balakin, I. V. Belokonov, et al.,
"Uncontrolled rotational motion of the satellite "Photon12"
and quasistatic microaccelerations on board,"
Kosmicheskie Issledovaniya, Vol. 41,
No. 1, pp. 4556, 2003. 
8.  A. A. Voronin and V. V. Sazonov,
"Periodic motions of gyroscopic systems,"
PMM [Applied Mathematics and Mechanics], Vol. 52, No. 5, pp. 719729,
1988. 

Received 
11 March 2003 
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