# Higher order resonance stability of triangular libration points for radiating primaries in ER3BP

## DOI:

https://doi.org/10.14419/ijaa.v3i1.4334## Published:

2015-03-24## Keywords:

ER3BP, Hamiltonian Functions, Triangular Libration Points, Resonance, KAM Theory.## Abstract

The main aim of this paper is to study the existence of resonance and stability of the triangular equilibrium points in the framework of ER3BP when both the attracting bodies are sources of radiation at w_{1}=w_{2}, w_{1}=2w_{2}, w_{1}=3w_{2} in both circular and elliptical cases .A practical application of this model could be seen in the case of binary systems ( Achird, Luyten, Î± Cen- AB, Kruger 60, Xi Bootis). The study is carried out both analytically and numerically by considering various values of radiation pressures and around binary systems .In both cases (CR3BP and ER3BP) it is found that w_{1}=w_{2} corresponds to the boundary region of the stability for the system, whereas the other two cases w_{1}=2w_{2}, w_{1}=3w_{2} Â correspond to the resonant cases. In order to investigate the stability, the Hamiltonian is normalized up to the fourth order by using linear canonical transformation of variables. Then KAM theorem is applied to investigate the stability for different values of radiation pressures in general and around the binary systems in particular. Finally, simulation technique is applied to study the correlation between radiation pressures and mass ratio in circular case; mass ratio and eccentricity in elliptical case. It is found that all the binary systems considered are stable. Also, it is found that except for some values of the radiation pressure parameters and for m<=m_{c} =0.0385209 the triangular equilibrium points are stable.

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