In this paper we are interested in studying some issues relating to the
general problem of locomotion by shape- changes in a two dimensional perfect
fluis. Our results are two folds: 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 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.