  We address the problem of controlling a dynamical system governing the motion
of a 3D weighted shape changing body swimming in a perfect fluid. The rigid
displacement of the swimmer results from the exchange of momentum between
prescribed shape changes and the flow, the total impulse of the fluid-swimmer
system being constant for all times. We prove the following tracking results:
(i) Synchronized swimming: Maybe up to an arbitrarily small change of its
density, any swimmer can approximately follow any given trajectory while, in
addition, undergoing approximately any given shape changes. In this statement,
the control consists in arbitrarily small superimposed deformations; (ii)
Freestyle swimming: Maybe up to an arbitrarily small change of its density, any
swimmer can approximately tracks any given trajectory by combining suitably at
most five basic movements that can be generically chosen (no macro shape
changes are prescribed in this statement).
