Stability in sense of Lyapunov of circular orbits in Manev potential

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.