Constant-speed ramps for a central force field

Abstract

We investigate the problem of determining the planar curves that describe ramps where a particle of mass m moves with constant-speed when is subject to the action of the friction force and a force whose magnitude F(r) depends only on the distance r from the origin. In this paper we describe all the constant-speed ramps for the case F(r) = -m/r. We show the circles and the logarithmic spirals play an important role. Not only they are solutions but every other solution approaches either a circle or a logarithmic spiral.