O. Miloni and S. Ferraz-Mello
Analytical Proper Elements for Hilda Asteroids



In this work we calculate analytically proper elements for asteroids in the 3:2 resonance with Jupiter, starting from the osculating elements. This is performed by the application of a new resonant perturbation theory (Ferraz-Mello, 1997, 2002) allowing the construction of formal solutions in cases where a resonance and long-period angles appear simultaneously. The disturbing function used was the Global expansion (Beaugé, 1996), adapted to include short period terms. The work is divided in the following parts: (i) passage from osculating to mean orbital elements by averaging over the short periods terms. (ii) Analytical integration of the Hori Kernel (pendulum model) over the librating resonant angle. (iii) Application of the resonant Lie series theory to obtain the mean-mean elements. (iv) Calculation of the proper momenta (and its associated "proper orbital elements") by elimination of the remaining angular variable.

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