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Celestial Mechanics and Dynamical Astronomy

, Volume 48, Issue 3, pp 267–288 | Cite as

Spectral stability of relative equilibria

  • James E. Howard
Article

Abstract

The spectral stability of synchronous circular orbits in a rotating conservative force field is treated using a recently developed Hamiltonian method. A complete set of necessary and sufficient conditions for spectral stability is derived in spherical geometry. The resulting theory provides a general unified framework that encompasses a wide class of relative equilibria, including the circular restricted three-body problem and synchronous satellite motion about an aspherical planet. In the latter case we find an interesting class of stable nonequatorial circular orbits. A new and simplified treatment of the stability of the Lagrange points is given for the restricted three-body problem.

Keywords

Stability satellite orbits three-body problem 

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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • James E. Howard
    • 1
  1. 1.Institute of Nonlinear Science and Physics DepartmentUniversity of CaliforniaSanta Cruz

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