Regularizations of string mechanics

We will discuss two examples of regularization in inextensible strings, as exemplified by chains or flexible cables, subject to gravity: (1) In the whipping of the free end of a falling string, velocity, acceleration, and tension follow predictable singular scalings until they peak at finite values that depend on the initial geometry. (2) In a loop of cable, the singular perturbation associated with bending elasticity allows a catenary to close upon itself; this example will clarify some misconceptions about "lariat chains" and "string shooters", in which inertia and drag are less important than they may seem.