Dynamics of cruising swimming by a deformable sphere for two simple models

The dynamics of periodic swimming is studied for two models of a deformable sphere, the dipole-quadrupole model and the quadrupole-octupole model. For the two models the solution of the Navier-Stokes equations can be found exactly to second order in the amplitude of stroke. Hence the oscillating force exerted by the fluid on the body is calculated. This allows calculation of the periodic time-dependent center of mass velocity.