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

The effect of perturbations in Coriolis and cetrifugal forces on the nonlinear stability of the equilibrium point of the Robe′s (1977) restricted circular three‐body problem has been studied when the density parameter K is zero. By applying Kolmogorov‐Arnold‐Moser (KAM) theory, it has been found that the equilibrium point is stable for all mass ratios μ in the range of linear stability 8/9 + (2/3)((43/25) ϵ 1 − (10/3) ϵ ) < μ < 1, where ϵ and ϵ 1 are, respectively, the perturbations in Coriolis and centrifugal forces, except for five mass ratios μ 1 =0.93711086 − 1.12983217 ϵ + 1.50202694 ϵ 1 , μ 2 = 0.9672922 − 0.5542091 ϵ + 1.2443968 ϵ 1 , μ 3 = 0.9459503 − 0.70458206 ϵ + 1.28436549 ϵ 1 , μ 4 = 0.9660792 − 0.30152273 ϵ + 1.11684064 ϵ 1 , μ 5 = 0.893981 − 2.37971679 ϵ + 1.22385421 ϵ 1 , where the theory is not applicable.

Abstract licence: CC BY

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