Effect of Perturbations in Coriolis and Centrifugal Forces on the Nonlinear Stability of Equilibrium Point in Robe's Restricted Circular Three-Body Problem

Abstract EN

The effect of perturbations in Coriolis and cetrifugal forces on the nonlinearstability of the equilibrium point of the Robe's (1977) restricted circularthree-body problem has been studied when the density parameter K is zero.

By applying Kolmogorov-Arnold-Moser (KAM) theory, it has been foundthat the equilibrium point is stable for all mass ratios μ in the range oflinear stability 8/9+(2/3)((43/25)ϵ1−(10/3)ϵ)<μ<1, where ϵ and ϵ1 are, respectively, the perturbations in Coriolis and centrifugal forces, except for five mass ratiosμ1=0.93711086−1.12983217ϵ+1.50202694ϵ1, μ2 = 0.9672922−0.5542091ϵ+ 1.2443968ϵ1, μ3=0.9459503−0.70458206ϵ+ 1.28436549ϵ1, μ4=0.9660792−0.30152273ϵ + 1.11684064ϵ1, μ5=0.893981−2.37971679ϵ + 1.22385421ϵ1, where the theory is not applicable.