On the stability of triangular Lagrangian points in the restricted three-body problem

摘要

explore the stability of triangular libration points in the spatial (three-dimensional) circular restricted three-body problem. For the analysis of stability, we derive new equations coupling up distances from an infinitesimally small particle to bodies with masses m(1) and m(2). We prove a theorem on the instability of triangular libration points and discuss relations between Lyapunov stability and Birkhoff stability.