Global Controllability for a “Rowing” Swimming Model

Abstract

We consider a swimmer whose body consists of three small narrow rectangles connected by flexible links. Our goal is to study its swimming capabilities when it applies a rowing motion in a fluid governed in a bounded domain by the nonstationary Stokes equation. Our approach explores an idea that a body in a fluid will move in the direction of least resistance determined by its geometric shape. Respectively, we assume that the means by which we can affect the motion of swimmer are the change of the spatial orientation of the aforementioned rectangles and the direction and strength of rowing motion. The main results are derived in the framework of mathematical controllability theory for pde’s and are based on a constructive technique allowing one to calculate an incrementalmotion of swimmer.