When fish Moonwalk

In this paper we study some issues relating to the general problem of locomotion by shape-changes in a perfect fluid. Our results are two fold. First we introduce a rigorous model for a weighted self-propelled swimming body - one specificity of this model being that the number of the body´s deformations degrees of freedom is infinite. The dynamic of the coupled system fluid-body is driven by the so-called Euler-Lagrange equations: a system of ODEs allowing us to compute the rigid motion of the body with respect to its prescribed shape-changes. Second, we prove controllability results for this model using powerful tools of geometric control theory. For instance, we show that the body can follow (approximately) any prescribed trajectory while undergoing (approximately) any prescribed shape-changes (this surprising phenomenon will be called Moonwalking). Most of our theoretical results are illustrated by numerical simulations.