  The swimming of an assembly of rigid spheres immersed in a viscous fluid of
infinite extent is studied in low Reynolds number hydrodynamics. The
instantaneous swimming velocity and rate of dissipation are expressed in terms
of the time-dependent displacements of sphere centers about their collective
motion. For small amplitude swimming with periodically oscillating
displacements, optimization of the mean swimming speed at given mean power
leads to an eigenvalue problem involving a velocity matrix and a power matrix.
The corresponding optimal stroke permits generalization to large amplitude
motion in a model of spheres with harmonic interactions and corresponding
actuating forces. The method allows straightforward calculation of the swimming
performance of structures modeled as assemblies of interacting rigid spheres. A
model of three collinear spheres with motion along the common axis is studied
as an example.
