Trajectories of $L_4$ and Lyapunov Characteristic Exponents in the Generalized Photogravitational Chermnykh-Like Problem

TL;DR

This paper investigates the chaotic behavior and stability of trajectories near the Lagrangian point L4 in a generalized photogravitational problem, analyzing Lyapunov exponents and the effects of various physical parameters.

Contribution

It introduces a detailed analysis of trajectory behavior and stability at L4 considering radiation, oblateness, and belt mass effects in a generalized model.

Findings

Trajectories near L4 follow epicycloid paths and spiral away.

Lyapunov exponents are positive, indicating chaos.

L4 remains asymptotically stable despite chaos.

Abstract

The dynamical behaviour of near by trajectories is being estimated by Lyapunov Characteristic Exponents(LCEs) in the Generalized Photogravitational Chermnykh-Like problem. It is found that the trajectories of the Lagrangian point $L_4$ move along the epicycloid path, and spirally depart from the vicinity of the point. The LCEs remain positive for all the cases and depend on the initial deviation vector as well as renormalization time step. It is noticed that the trajectories are chaotic in nature and the $L_4$ is asymptotically stable. The effects of radiation pressure, oblateness and mass of the belt are also examined in the present model.