Morse index of circular solutions for repulsive central force problems on surfaces

Abstract The classical theory of repulsive central force problem on the standard (flat) Euclidean plane can be generalized to surfaces by reformulating the basic underlying physical principles by means of differential geometry. The aim of the present paper is to compute the Morse index of the circular periodic orbits in the case of repulsive power-law potentials of the Riemannian distance on revolution’s surfaces.