  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.
