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

Abstract

This paper analyses the local bifurcation of linear stability of motion near the triangular equilibrium points in the neighborhood of parametric resonance frequency ω2 = for circular and elliptic orbits, respectively. The Hamiltonian is made independent of time using canonical transformations.It is found that the values of mass ratio, µ are less than the critical value µc in resonant case, for both orbits. The boundary of the stability region are found in form of equations for both orbits, circular and elliptic (for small values of e). The regions of stability and instability are plotted in the graphs. There is a shift in the bifurcation points of mass ratio,µ from the critical value µc as a result of increase in values of radiation pressure(δ), triaxiality parameters(σ1 and σ2).