Snapping of strings: singular or just really big?

The whipping of the free end of a string, chain, or flexible cable, induced by generic initial and boundary conditions, is a rapid event featuring a tension spike and significant focusing of kinetic energy. It has been suggested that this "snapping" event is a regularized singularity. We examine the particular case where the system is driven by gravity and the initial conditions are a catenary, for which prior experimental data exist. We simulate an inextensible string by converting the usual partial-differential-algebraic system into a partial-ordinary-differential system and solving this with a finite difference scheme. This accurately reproduces the available experimental position data without any fitting parameters or ad hoc damping, and thus provides a more realistic estimate of forces, velocities, and accelerations. Our results reveal accelerations several orders of magnitude greater than the driving acceleration, associated with a very steep tension gradient near the free end of the body. By seeing how these quantities scale with the fineness of the numerical mesh, we conclude that while the amplification of some quantities is remarkably large, the event is only potentially singular when a geometric singularity is supplied by a perfectly folded vertical initial condition. Time permitting, we will comment on extensible cables and bungee jumping.