Existence of Resonance Stability of Triangular Equilibrium Points in Circular Case of the Planar Elliptical Restricted Three-Body Problem under the Oblate and Radiating Primaries around the Binary System

Abstract

This paper analyzes the existence of resonance stability of the triangular equilibrium points of the planar elliptical restricted three-body problem when both the primaries are oblate spheroid as well as the source of radiation under the particular case, whene=0. We have derived Hamiltonian function describing the motion of infinitesimal mass in the neighborhood of the triangular equilibrium solutions taken as a convergent series. Hamiltonian function for the system has been derived and also expanded in powers of the generalized components of momenta. We have used canonical transformation to make the Hamiltonian function independent of true anomaly. The most interesting and distinguishable results of this study are establishing the relation for determining the range of stability at and near the resonanceω2=1/2around the binary system.

Analysis on nonlinear stability of the triangular libration points for radiating and oblate primaries in ER3BP

“…The differential equations of the motion of the infinitesimal mass in elliptical restricted three body problem under radiating primaries in pulsating system as given by Narayan and Shrivastava [27] is:…”

“…. The coordinates of the triangular equilibrium points L4 and L5 as given by: Narayan and Shrivastava [27] …”

Bifurcation Analysis of Stability of Triangular Equilibrium Points in the Elliptic Restricted Problem of Three Bodies

“…Now, using the transformations given in the (19), (20) and (21) in the above equation. The normalised Hamiltonian can be written as:…”

Nonlinear Stability of the Triangular Libration Points for Radiating and Oblate Primaries in CR3BP in Nonresonance Condition

“…The differential equations of the motion of the infinitesimal mass in elliptical restricted three-body problem under radiating primaries in pulsating system as given by Narayan and Shrivastava [27] are…”