  We reconsider fluid dynamics for a self-propulsive swimmer in Stokes flow.
With an exact definition of deformation of a swimmer, a proof is given to
Purcell's scallop theorem including the body rotation. The breakdown of the
theorem due to a finite Stokes number is discussed by using a perturbation
expansion method and it is found that the breakdown generally occurs at the
first order of the Stokes number. In addition, employing the Purcell's
"scallop" model, we show that the theorem holds up to a higher order if the
strokes of the swimmer has some symmetry.
