The Dynamics and Kinematics of Swimming

The motion of biological systems in fluids is inherently complex, even for the simplest organisms. In this talk, we develop methods to analyze locomotion of both mechanical and biological systems with the aim of rationalizing biology and informing robotic design. We begin by building a visualization framework studying an idealized swimmer, Purcell's three link swimmer, at low Reynolds number. This framework allows us to illustrate the complete dynamics of the system, efficiently design gaits for motion planning, and identify optimal gaits in terms of efficiency and speed. We extend the three-link case to a serpenoid swimmer, or a swimmer with a continuously deformable shape.  

Drawing on the principles behind representing the serpenoid swimmer's shape, we develop a method based on proper orthogonal decomposition (POD) that describes the motion of complex biological systems in a low order manner, so that using only two degrees of freedom adequately describes the animal's motion. We successfully apply this method to species in both high and low Reynolds environments to elucidate different phenomena, including chemotaxing (movement owing to the presence of an attractant), inter- and intra-species comparison in sea urchin spermatozoa and bull spermatozoa, and kinematic responses to increasing viscosity in C. elegans (nematodes). We successfully illustrate the generalized utility of our decomposition method, combined with our visualization framework, to explore and understand fundamental kinematics of a wide range of both natural and man-made systems.