Determination of Libration Characteristics of Asteroids near Mean Motion Commensurabilities 1/1, 4/3, 3/2, 2/1, 7/3, 5/2, and 3/1

Abstract

The possibility of using a generalized perfect resonance for the study of libration motions of asteroids near the (p + q)/p-type commensurabilities of the mean motions of asteroids and Jupiter is considered. Based on the equations of the planar circular restricted three-body problem, the libration-motion equations are derived and their solutions for the intermediate Hamiltonian, as well as a solution taking into account perturbations of the order O(m 3/2), are determined.