Generic controllability of 3D swimmers in a perfect fluid

摘要

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, with the total impulse of the fluid-swimmer system being null at every time. We prove the following tracking results: (i) Synchronized swimming: 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: Up to an arbitrarily small change of its density, any swimmer can approximately track any given trajectory by suitably combining at most five basic movements that can be generically chosen (no macro shape changes are prescribed in this statement).