Effect of Perturbations in Coriolis and Centrifugal Forces on the Non-Linear Stability of <i>L</i>₄ in the Photogravitational Restricted Three Body Problem

Abstract

Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L 4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triaxial rigid bodies) and the bigger primary is a source of radiation. Moser’s conditions are utilized in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff’s normal form with the help of double D’Alembert’s series. It is found that L 4 is stable for all mass ratios in the range of linear stability except for the three mass ratios μ c1 , μ c2 and μ c3 , which depend upon the perturbations ε 1 and ε 1 in the Coriolis and centrifugal forces respectively and the parameters A 1 , A 2 , A 3 and A 4 which depend upon the semi-axes a 1 ,b 1 ,c 1 ;a 2 ,b 2 ,c 2 of the triaxial rigid bodies and p, the radiation parameter.