Sufficient and necessary conditions for the stability of the libration points in the perturbed circular restricted three-body problem and their applications

Sufficient and necessary conditions for the stability of the libration points in the perturbed circular restricted three-body problem are given. The conditions are in terms of the coefficients of the characteristic equations of the variational equations of the libration points, and can be used very conveniently. The effect of the perturbation of an arbitrary external force on the stability of the triangular libration points in the classical circular restricted three-body problem and the effect of the perturbation of the inertial drag on the stability of the principal libration points in the Robe circular restricted three-body problem are discussed by taking advantage of the obtained conditions.