  We consider a two-dimensional, incompressible fluid body, together with
self-induced interactions. The body is perturbed by an external particle with
small mass. The whole configuration rotates uniformly around the common center
of mass. We construct solutions, which are stationary in a rotating coordinate
system, using perturbative methods. In addition, we consider a large class of
internal motions of the fluid. The angular velocity is related to the position
of the external particle and is chosen to satisfy a non-resonance condition.
