Constant Speed Ramps

Abstract

In this paper we show all possible ramps where an object can move with constant speed under the effect of gravity and friction. The planar ramp are very easy to describe, just rotate a curve with velocity vector (tanh(as),sech(as)). Recall that tanh(as)^2+sech^2(as) = 1. Therefore, the solution of the planar constant speed problem is connected with easy to describe examples of curves with arc-length parameter. For ramps in the space, we show that there are as many ramps as tangent unit vector fields in the south hemisphere. A video explaining these results can be found at http://www.youtube.com/watch?v=iBrvbb0efVk