Inertial dynamics of chains: slack, stress, and convective instabilities

Inertial chains may be thought of as one-dimensional incompressible/inextensible fluids or solids moving in three dimensions. Incompressibility is enforced by a stress screened by the chain's curvature (slack). The nature of the stress--- tensile or compressive, uniform or spatially varying--- governs the stability of the motion. The most stable motions, characterized by a uniform tensile stress, belong to a wide class that includes travelling waves of curvature and torsion. Convective instabilities exist in the presence of stress gradients; we present a striking example from a tabletop experiment involving a growing arch in a straightening chain. This work adds to a large body of literature on locally arc length preserving dynamics of curves arising in the study of thin objects such as elastic rods, vortex filaments, and oceanic jets.