Performing Floquet stability test for AEPs and exploring pulsating ZVCs in the perturbed planar elliptic solar sail problem

Abstract

The study of stability properties of equilibrium points is a key task to know the behaviour of a dynamical system, in space. This paper deals about a perturbed solar sail problem under the frame of planar elliptic restricted three-body problem in the context of artificial equilibrium points (AEPs), pulsating zero velocity curves (ZVCs) and Floquet stability analysis. First, the proposed problem is formulated under the influence of oblateness of both the primaries, sail lightness number and presence of a disc with density profile and all the AEPs are determined. It is found that due to these perturbations, positions of all the AEPs either shift towards the origin or move away from it. Further, pulsating ZVCs are estimated by establishing an invariant relation and it is seen that impacts of the assumed perturbing factors are very less on the prohibited zones for the motion solar sail. Finally, Floquet stability analysis is performed for all the AEPs with the help of characteristic exponents and transition curves. It is observed that changes in the values of perturbing parameters cause changes in the stability regions as well as position of the bifurcation point on the \(\mu\)-axis of the transition curve. These results can be utilised to study the more generalised solar sail problem in the presence of other kinds of perturbations.