Abstract
We consider the system of planetary rings with shepherds as a restricted three or four-body problem, neglecting interactions between ring particles. We show that the generic occurrence of rings for the case of rotating short-range potentials can be extended to the case of gravitational potentials. The consecutive collision periodic orbits created by saddle-center bifurcations are of central importance.
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Benet, L. Occurrence of Planetary Rings with Shepherds. Celestial Mechanics and Dynamical Astronomy 81, 123–128 (2001). https://doi.org/10.1023/A:1013371423194
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DOI: https://doi.org/10.1023/A:1013371423194