Moving Forward by Shaking Sideways

Abstract

We investigate a simple model for a self-propelled swimmer, which consists of a fluctuating force acting at a point on a rigid body. The rigid body is subject to Newton’s equations with linear friction, corresponding to drag in a viscous fluid. The force has zero time average, so net motion is challenging. We show that the swimmer can inch forward by shaking from side to side and exploiting friction coupled with nonlinearity. For large enough forcing amplitude it can reverse direction and swim backward.