The swimming of a deformable uniform sphere is studied in second order
perturbation theory in the amplitude of the stroke. The effect of the first
order reaction force on the first order center of mass velocity is calculated
in linear response theory by use of Newton's equation of motion. The response
is characterized by a dipolar admittance, which is shown to be proportional to
the translational admittance. As a consequence the mean swimming velocity,
calculated in second order perturbation theory, depends on the added mass of
the sphere. The mean swimming velocity and the mean rate of dissipation are
calculated for several selected strokes.Comment: 20 pages, 15 figure
