We describe a model for the planar locomotion of a free deformable hydrofoil in an infinite fluid. The time-varying shape of the foil is obtained as the image of a circle in the complex plane under a time-varying conformal transformation. The fluid is assumed to be incompressible and inviscid, but a mechanism is introduced whereby the foil can shed discrete vorticity from its trailing edge in accordance with a periodically enforced Kutta condition. Vortex shedding provides a propulsive force as a consequence of the conservation of impulse in the system; we compare the influence of this force on the model to forces arising in true inviscid locomotion. Simulations based on this model qualitatively reproduce the planar dynamics of swimming marine animals. We demonstrate that the model possesses an explicit Hamiltonian structure in between vortex shedding events, examine the energetics of certain motion primitives, and discuss an approach to model reduction through the assumption of a simplified wake.

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