  Due to the kinematic reversibility of Stokes flow, a body executing a
reciprocal motion (a motion in which the sequence of body configurations
remains identical under time reversal) cannot propel itself in a viscous fluid
in the limit of negligible inertia; this result is known as Purcell's scallop
theorem. In this limit, the Reynolds numbers based on the fluid inertia and on
the body inertia are all zero. Previous studies characterized the breakdown of
the scallop theorem with fluid inertia. In this paper we show that, even in the
absence of fluid inertia, certain dense bodies undergoing reciprocal motion are
able to swim. Using Lorentz's reciprocal theorem, we first derive the general
differential equations that govern the locomotion kinematics of a dense
swimmer. We demonstrate that no reciprocal swimming is possible if the body
motion consists only of tangential surface deformation (squirming). We then
apply our general formulation to compute the locomotion of four simple
swimmers, each with a different spatial asymmetry, that perform normal surface
deformations. We show that the resulting swimming speeds (or rotation rates)
scale as the first power of a properly defined "swimmer Reynolds number'',
demonstrating thereby a continuous breakdown of the scallop theorem with body
inertia.
