Floquet stability analysis of equilibrium points and numerical exploration of pulsating zero-velocity curves and Newton–Raphson basins of attraction

Abstract

An important and pivot aspect of a dynamical system is the stability property and its range, which play a crucial role towards the stabilisation of a mission design. Present paper deals with Floquet stability analysis of equilibrium points and estimation of pulsating zero velocity curves and Newton–Raphson basins of attraction associated to these equilibrium points under the radiation pressure effect in the photo-gravitational planar elliptic restricted four body problem. Floquet stability test for the equilibrium points is performed with the help of the transition curves, which are generated under the influence of radiation pressure. It is noticed that stability range of the respective equilibrium points have deviated due to radiation pressure. To observe the possible regions of motion for restricted body, the pulsating zero velocity curves are numerically explored after establishing an invariant relation. It is found that not only the radiation parameter but also eccentricity and true anomaly reflect a considerable impact on the shape and size of forbidden regions. To see the tendency of randomly selected points in the phase space, Newton–Raphson basins of attraction associated to each attractor are estimated and effects of perturbing parameters are analysed. It is observed that effects of radiation and mass parameters are considerable however, that of eccentricity and true anomaly are negligible. Moreover, from probability distribution bar diagram, most probable number of iterations is 10 for the case when two primaries are of equal masses and third one is different, whereas it is 20 for the case when all primaries are of identical mass. These results will be helpful to study the generalised problem along with other kind of perturbations.