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| Systems comprising free solid bodies interacting with singular distributions of vorticity in two- and three-dimensional ideal fluids exhibit noncanonical Hamiltonian structures. Velocity constraints like the classical Kutta condition can be imposed on such systems discretely or continuously in time to model localized boundary layer detachment and vortex shedding in an idealized way. This approach provides a basis for the reduced-order modeling of biological and robotic locomotion in viscous fluids. This talk will detail a selection of models obtained in this way, addressing the role played by symmetry breaking in enabling locomotion and the integrability of the constraints in question. |
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