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Celestial Mechanics and Dynamical Astronomy

, Volume 85, Issue 1, pp 51–66 | Cite as

On the Stability of Planar Oscillations and Rotations of a Satellite in a Circular Orbit

  • Anatoliy P. Markeev
  • Boris S. Bardin
Article

Abstract

We deal with the stability problem of planar periodic motions of a satellite about its center of mass. The satellite is regarded a dynamically symmetric rigid body whose center of mass moves in a circular orbit.

By using the method of normal forms and KAM theory we study the orbital stability of planar oscillations and rotations of the satellite in detail. In two special cases we investigate the orbital stability analytically by introducing a small parameter. In the general case, numerical calculations of Hamiltonian normal form are necessary.

planar oscillations and rotations normal form stability parametric resonance 

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References

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Anatoliy P. Markeev
    • 1
  • Boris S. Bardin
    • 2
  1. 1.Institute for Problems in MechanicsRussian Academy of SciencesMoscowRussia, e-mail
  2. 2.Department of Theoretical MechanicsFaculty of Applied Mathematics, Moscow Aviation InstituteMoscowRussia, e-mail

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