On the locomotion and control of a self-propelled shape-changing body in a fluid

Thomas Chambrion (1, 2) , Alexandre Munnier (1, 2)

1 CORIDA - Robust control of infinite dimensional systems and applications
2 IECN - Institut Élie Cartan de Nancy

In this paper we study the locomotion of a shape-changing body swimming in a two-dimensional perfect fluid of infinite extent. The shape-changes are prescribed as functions of time satisfying constraints ensuring that they result from the work of internal forces only: conditions necessary for the locomotion to be termed self-propelled. The aim of this paper is several folds: First, it contains a rigorous framework for the study of animal locomotion in fluid. Second, it makes clear the connection between shape-changes and internal forces. Third, it contains the first theoretical result (to our knowledge) of control for a swimming body in an ideal fluid.

Mots clés: Locomotion; biomechanics; ideal fluid; geometric control theory

Domaines: Optimisation et contrôle [math.OC]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Thomas Chambrion, Alexandre Munnier. On the locomotion and control of a self-propelled shape-changing body in a fluid. 2009. ⟨hal-00422429v1⟩