Periodic Orbits in the Full Two Body Problem

Details Periodic Orbits in the Full Two Body Problem Periodic Orbits in the Full Two Body Problem

Jul 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007dda....38.1402b&link_type=abstract

American Astronomical Society, DDA meeting #38, #14.02

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Scientific paper

The idealized problem of a binary asteroid system dynamics is studied. As the non-spherical mass distribution of one of the bodies is considered, the problem is referred as the Full Two Body Problem (F2BP). The current work investigates the stability of relative equilibria for an ellipsoid-sphere system at given values of angular momentum and the associated periodic orbit families that arise from these points. For a given value of angular momentum, we show that there are in general two relative equilibrium solutions which are opposite in stability. As the non-equilibrium problem is more common in nature, we also investigate periodic orbit families in the F2BP that emanate from the relative equilibrium. We can find two stable families in the vicinity of a stable relative equilibrium and one unstable family associated to the unstable relative equilibrium. The periodic orbits are computed using a Poincare map reduction method on a two degree of freedom Hamiltonian system. The minimum energy point of these periodic orbit families terminates in the relative equilibrium conditions. An approximation method was derived in order to facilitate the computation of periodic orbits near relative equilibria while keeping the interesting dynamical features. We show results on relative equilibria, periodic orbits, and their stability.
The authors thank the Jet Propulsion Laboratory/California Institute of Technology and the Natural Sciences and Engineering Research Council of Canada for their support.

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