Author(s)

Kavita Chauhan^1*, S. N. Rai², Rajiv Aggarwal³

¹Department of P. G. Department of Mathematics, V.K.S. University, Ara, India.
²Department of Department of Mathematics, S.B. College, Ara, India.
³Department of Mathematics, Sri Aurobindo College, University of Delhi, Delhi, India.

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 μ_c1, μ_c2 and μ_c3, 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.

Restricted Three Body Problem, Axis Symmetric Bodies; Non-Linear Stability, Libration Point L₄, Double D’Alembert’s Series Method

Chauhan, K. , Rai, S. and Aggarwal, R. (2015) Effect of Perturbations in Coriolis and Centrifugal Forces on the Non-Linear Stability of L₄ in the Photogravitational Restricted Three Body Problem. International Journal of Astronomy and Astrophysics, 5, 275-290. doi: 10.4236/ijaa.2015.54031.