Effect of Perturbations in Coriolis and Centrifugal Forces on the Non-Linear Stability of iL/isub4/subin the Photogravitational Restricted Three Body Problem

摘要

Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 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 L4 is stable for all mass ratios in the range of linear stability except for the three mass ratios μc1, μc2 and μc3, which depend upon the perturbations ε1 and ε1 in the Coriolis and centrifugal forces respectively and the parameters A1,A2,A3 and A4 which depend upon the semi-axes a1,b1,c1;a2,b2,c2 of the triaxial rigid bodies and p, the radiation parameter.