Characteristic exponents for the triangular points in the elliptic restricted problem of three bodies

摘要: D ANBY3 studied the linear stability of triangular points numerically using Floquet theory. He presented transition curves that separate stable from unstable orbits in fj,-e plane (JJL is ratio smaller primary to sum masses two primaries, and e eccentricity primaries' orbit). These intersect ju axis at a juo, where ju0 = 0.03852 limiting value /z for circular case, /z0 0.02859 JJL such one periods motion about exactly twice period orbit primaries case. Bennett2 obtained first-order complicated analytical expression JJLQ an technique determination characteristic exponents. Alfriend Rand1 second-order expressions \ia JLIO method multiple scales.5"7 Nayfeh Kamel8 determined fourth-order carves perturbation technique. In this Note, we obtain exponents theory9 used by Whittaker10 treatment Mathieu equation. We use same formulation Refs. 1 8. The first variational equation can be transformed into