  Translational and rotational swimming at small Reynolds number of a planar
assembly of identical spheres immersed in an incompressible 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 translational and rotational swimming velocities of the assembly are
deduced from momentum and angular momentum balance equations. The mean power
required during a period is calculated from an instantaneous power equation.
Expressions are derived for the mean swimming velocities and the power, valid
to second order in the amplitude of displacements from the relative equilibrium
positions. Hence these quantities can be evaluated for prescribed periodic
displacements. Explicit calculations are performed for three spheres
interacting such that they form an equilateral triangle in the rest
configuration.
