  Motivated by the swimming of sperm in the non-Newtonian fluids of the female
mammalian reproductive tract, we examine the swimming of filaments in the
nonlinear viscoelastic Upper Convected Maxwell model. We obtain the swimming
velocity and hydrodynamic force exerted on an infinitely long cylinder with
prescribed beating pattern. We use these results to examine the swimming of a
simplified sliding-filament model for a sperm flagellum. Viscoelasticity tends
to decrease swimming speed, and changes in the beating patterns due to
viscoelasticity can reverse swimming direction.
