Tautochrone curve of a rotating modified Keplerian field

Abstract

A tautochrone is a curve in a plane such that the time required for a particle to slide down the curve to its lowest point under an external field is independent of its initial position on the curve. Using fractional calculus, we determine the tautochrone curve for a system subject to a Keplerian field with an inverse-square correction which may due to the general relativistic effect. The effect of rotation is also included in the analysis.