In this article, we are interested in studying locomotion strategies for a
class of shape-changing bodies swimming in a fluid. This class consists of
swimmers subject to a particular linear dynamics, which includes the two most
investigated limit models in the literature: swimmers at low and high Reynolds
numbers. Our first contribution is to prove that although for these two models
the locomotion is based on very different physical principles, their dynamics
are similar under symmetry assumptions. Our second contribution is to derive
for such swimmers a purely geometric criterion allowing to determine wether a
given sequence of shape-changes can result in locomotion. This criterion can be
seen as a generalization of Purcell's scallop theorem (stated in Purcell
(1977)) in the sense that it deals with a larger class of swimmers and address
the complete locomotion strategy, extending the usual formulation in which only
periodic strokes for low Reynolds swimmers are considered.Comment: 14 pages, 10 figure
