The swimming of animalcules

Animalcules can swim in a viscous fluid at low Reynolds number and low Stokes number by moving their body parts in a periodic coherent fashion. The swimming motion is analyzed in a simple model of beads subject to periodic one-body forces. In the model the animalcule is held together by reactive two-body forces. The nonlinear equations of Stokesian dynamics are formulated on the basis of the Oseen tensor. Under suitable conditions the solution of the equations of motion has a limit cycle character. The limit cycle is analyzed for small amplitude motion in the framework of a bilinear theory. The linearized equations of motion are solved analytically for longitudinal and transverse modes of motion for a linear trimer, and expressions are derived for the swimming velocity and the mean dissipation to second order in the force amplitude. The results of the bilinear theory are compared to numerical solution of the nonlinear equations of motion. A similar comparison is made for chains of twelve beads.