Abstract
In this paper, we present the mathematical basis for the calculation of proper elements for asteroids in 3:2 mean-motion resonance with Jupiter from their osculating Keplerian elements. The method is based on a new resonant Lie-series perturbation theory (Ferraz-Mello, 1997, 2002), which allows the construction of formal solutions in cases where resonant and long-period angles appear simultaneously. For the disturbing function, we used the Beauge’s expansion (Beauge, 1996), adapted to include short period terms. In this paper, the theory is restricted to the planar case and only the perturbations due to Jupiter are considered.
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