Chambrion, Thomas; Munnier, Alexandre Generic controllability of 3D swimmers in a perfect fluid. (English) Zbl 1320.76131 SIAM J. Control Optim. 50, No. 5, 2814-2835 (2012). Summary: 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). Cited in 16 Documents MSC: 76Z10 Biopropulsion in water and in air 76B75 Flow control and optimization for incompressible inviscid fluids 92C10 Biomechanics Keywords:locomotion; geometric control; synchronized swimming; freestyle swimming; shape-changing body PDFBibTeX XMLCite \textit{T. Chambrion} and \textit{A. Munnier}, SIAM J. Control Optim. 50, No. 5, 2814--2835 (2012; Zbl 1320.76131) Full Text: DOI arXiv