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.
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Howard, J.E. Spectral stability of relative equilibria. Celestial Mech Dyn Astr 48, 267–288 (1990). https://doi.org/10.1007/BF02524333
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DOI: https://doi.org/10.1007/BF02524333