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O. Olsen (ITA)
ESA's upcoming Rosetta mission and NASA's NEAR mission have made it interesting to study orbits around rotating non symmetric objects. For simplicity, only the C20 and C22 parts of the potential are included. The potential is expanded in a Fourier-series in the Poincare variables. A canonically invariant perturbation theory as derived by Deprit, Cel. Mech, 1:12, 1969, is used to derive a secular theory valid near resonances of the form 2w\approx N\,n, where N is an integer, w is the angular velocity of the rotating nucleus and n is the mean motion of the orbiter. The theory is easily extended to other resonances.
This secular Hamiltonian is used to derive the location of stable fixed points in the averaged phase space. With the help of the canonical invariant perturbation theory, the location of the fixed points in the instantaneous phase space is recovered. These orbits' long term evolution is checked by numerical integration of the equations of motion.
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