Geometric Mechanics and Aquatic Locomotion through Vortex Shedding

The controlled shedding of vorticity and the resulting development of liftlike forces on control surfaces are fundamental to the hydrodynamics of macroscopic marine animals and underwater vehicles alike. Computational models can reproduce these phenomena with high fidelity, but such models are largely incompatible with analytical methods of model-based feedback control design. Problems in aquatic locomotion have recently attracted attention within the analytical mechanics community, leading to the framing of such problems in the context of Lagrangian systems and geometric nonlinear control, but efforts in this area have been limited to idealized problems in which vortex shedding is conspicuously absent. This paper describes preliminary work to extend the language of geometric mechanics to address the effects of vortex shedding implicitly by modeling the development of liftlike forces on self-propelling bodies.