  We consider a simple model of an internally driven self-rotating object; a
rotor, confined to two dimensions by a thin film of low Reynolds number fluid.
We undertake a detailed study of the hydrodynamic interactions between a pair
of rotors and find that their effect on the resulting dynamics is a combination
of fast and slow motions. We analyse the slow dynamics using an averaging
procedure to take account of the fast degrees of freedom. Analytical results
are compared with numerical simulations. Hydrodynamic interactions mean that
while isolated rotors do not translate, bringing together a pair of rotors
leads to motion of their centres. Two rotors spinning in the same sense rotate
with an approximately constant angular velocity around each other, while two
rotors of opposite sense, both translate with the same constant velocity, which
depends on the separation of the pair. As a result a pair of counter-rotating
rotors are a promising model for controlled self-propulsion.
