Locomotion and control of a self-propelled shape-changing body in a fluid

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

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

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; ideal fluid; geometric control theory; biomechanics

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

Thomas Chambrion, Alexandre Munnier. Locomotion and control of a self-propelled shape-changing body in a fluid. Journal of Nonlinear Science, 2011, 21 (3), pp.325-385. ⟨10.1007/s00332-010-9084-8⟩. ⟨hal-00422429v2⟩