Flexive and Propulsive Dynamics of Elastica at Low Reynolds Number

A stiff one-armed swimmer in glycerine goes nowhere. However, if its arm is elastic, the swimmer can go on its way. Quantifying this observation, we study a hyperdiffusion equation for the shape of the elastica in a viscous fluid, 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 experiments measuring biopolymer bending moduli to instabilities of twisted elastic filaments.