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A. Simula, F. Roig, S. Ferraz-Mello (IAG/USP)
The modelling of the resonant asteroidal dynamics has been recently improved by the use of the high-eccentricity non-planar asymmetric expansion. This second-degree expansion gives in explicit form the averaged potential of the perturbing forces acting on an asteroid in a first-order mean motion resonance. A reducing transformation is used to include the lowest degree effect of the perturber's eccentricity in the main part of the Hamiltonian. The re-organization of the terms of the Hamiltonian gives an abridged system able to represent the dynamics of the resonant asteroidal libration, plus higher order perturbation terms, including the secular effects of the perturber's eccentricity and inclination. This averaged Hamiltonian can be used for the computation of resonant proper elements by means of Hori's perturbative scheme. The key element is the use of an intermediary, both eccentric and inclined, Hori's kernel much richer than the usual ones, because it reproduces the properties of the whole system: the stationary points, the topology and the fundamental frequencies. And moreover, it includes the main secular effects of the perturber's eccentricity, providing a high realistic zero order solution.
This Hori's scheme can be applied also in the computation of proper elements for near-resonant asteroids, especially in the case of apocentric librations/circulations. Some preliminary results are shown in the case of the group of Cybelle, located at the right hand side of the 2:1 resonance with Jupiter.
This research was sponsored by F.A.P.E.S.P.
The author(s) of this abstract have provided an email address for comments about the abstract: simula@orion.iagusp.usp.br