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

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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.

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Authors and Affiliations

  1. Institute for Problems in Mechanics, Russian Academy of Sciences, Vernadsky ave. 101, Moscow, 117526, Russia, e-mail

    Anatoliy P. Markeev

  2. Department of Theoretical Mechanics, Faculty of Applied Mathematics, Moscow Aviation Institute, 4 Volokolamskoe Shosse, Moscow, 125871, Russia, e-mail

    Boris S. Bardin

Authors
  1. Anatoliy P. Markeev
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  2. Boris S. Bardin
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Markeev, A.P., Bardin, B.S. On the Stability of Planar Oscillations and Rotations of a Satellite in a Circular Orbit. Celestial Mechanics and Dynamical Astronomy 85, 51–66 (2003). https://doi.org/10.1023/A:1021739407472

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  • DOI: https://doi.org/10.1023/A:1021739407472

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