Resonance Stability of Oblate Infinitesimal in the Neighbourhood of Triangular Equilibrium Points for Triaxial Primaries in the Elliptic Restricted Three Body Problem (Journal of Informatics and Mathematical Sciences, 2022)
The present study aims to investigates the existence of resonance and linear stability of oblate infinitesimal in the neighbourhood of triangular equilibrium points of the elliptical restricted three body problem, considering effect of triaxial primaries in circular and elliptical cases. For this the Hamiltonian function, convergent in nature and describing the motion of the infinitesimal body in the neighbourhood of the triangular equilibrium solutions is derived. Also, the Hamiltonian for the system is expanded in powers of the generalized components of momenta. Further, canonical transformation has also been used to study the stability of the triangular equilibrium points. The study primarily focuses on establishing the relation for determining the range of stability at and near the resonance frequency at \(ω _2 =\frac{1}{2}\). It is observed that the parametric resonance is only possible at the resonance frequency \(ω _2 =\frac{1}{2}\) in circular and elliptical cases.