This talk is devoted to the mathematical investigation of the motion of a rigid body in an infinite Navier-Stokes liquid, under the action of a time-periodic driving mechanism. This latter can be, for example, a time-periodic force acting along a given constant direction, or time-periodic boundary data.

The main objective is to find conditions under which the body is propelled by the driving mechanism, namely, conditions that ensure that the body can cover a given trajectory in a finite time interval.