Effect of Perturbations in Coriolis and Centrifugal Forces on the Non-Linear Stability of L4 in the Photogravitational Restricted Three Body Problem ()
Kavita Chauhan1*,
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.
DOI: 10.4236/ijaa.2015.54031
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Abstract
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.
Share and Cite:
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.
Conflicts of Interest
The authors declare no conflicts of interest.
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