Flexive and Propulsive Dynamics of Elastica at Low Reynolds Numbers

A stiff one-armed swimmer in glycerine goes nowhere, but if its arm is elastic, exerting a restorative torque proportional to local curvature, the swimmer can go on its way. Considering this happy consequence and the principles of elasticity, we study a hyperdiffusion equation for the shape of the elastica in viscous flow, find solutions for impulsive or oscillatory forcing, and elucidate relevant aspects of propulsion. These results have application in a variety of physical and biological contexts, from dynamic biopolymer bending experiments to instabilities of elastic filaments.