  Swimming at small Reynolds number of a linear assembly of identical spheres
immersed in a viscous fluid is studied on the basis of a set of equations of
motion for the individual spheres. The motion of the spheres is caused by
actuating forces and forces derived from a direct interaction potential, as
well as hydrodynamic forces exerted by the fluid as frictional and added mass
hydrodynamic interactions. The swimming velocity is deduced from the momentum
balance equation for the assembly of spheres, and the mean power required
during a period is calculated from an instantaneous power equation. Expressions
are derived for the mean swimming velocity and the mean power, valid to second
order in the amplitude of displacements from the relative equilibrium
positions. Hence these quantities can be evaluated in terms of prescribed
periodic displacements. Explicit calculations are performed for a linear chain
of three identical spheres.
