Parametric Resonance Stability of Triangular Equilibrium Points of the Planar Elliptical Restricted Three-Body Problem around the Primaries of Oblate Spheroid

摘要

In this paper the effect of the primaries on the parametric resonance stability of the triangular equilibrium points of the planar elliptical restricted three body problem have been studied. We have derived the Hamiltonian for the system and expanded in powers of the generalized components of momenta. We have used canonical transformation due to Markeev (1971) to make the Hamiltonian independent of true anomaly, we have established a relation for determining the range of stability, near the parametric resonance at ω_2 =1/2 .