Geometry of whips and chains

Abstract

We study the geometry of the inextensible string (the whip) and its discrete approximation (the chain). In the absence of gravity, both motions represent geodesic motions on certain manifolds. We show how the motion of the chain converges to that of a whip, and how the curvature of the chain's configuration space converges to that of the whip's configuration space. Finally we speculate on the analogous approximation of an incompressible fluid by a discrete system.