Stability in sense of Lyapunov of circular orbits in Manev potential

TL;DR

This paper investigates the stability of circular orbits in a Manev potential, demonstrating their Lyapunov stability using a constructed Lyapunov function and comparing results with Newtonian gravity.

Contribution

It introduces a Lyapunov function-based method to prove the stability of circular orbits in Manev potential, extending classical gravitational stability analysis.

Findings

Circular orbits in Manev potential are Lyapunov stable.

A positive definite Lyapunov function was constructed for the Manev two-body problem.

Stability results are compared with Newtonian gravitational orbits.

Abstract

In this article we consider the motion of two bodies under the action of a Manev central force. We obtain the radius of the circular orbit and analyze its stability in sense of Lyapunov. Drawn on the first integrals of angular momentum and energy, we build a positive definite function which satisfies the Lyapunov's theorem of stability. The existence of the Lyapunov function prove that the circular orbits in Manev two body problem are stable at any perturbation. In the end we compare these results with those valid for the circular orbits in the Newtonian gravitational field.