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| We consider a one-dimensional swimmer in an infinite viscous fluid. An appealing mathematical framework is described to study the equations of motion. We prove that the motion of the swimmer is uniquely determined by the history of its shapes. Furthermore, we address the problem of controllability of the swimmer, by using elements of control theory, and we prove the existence of optimal (i.e., power minimizing) swimming strategies.
We also present a numerical approach to the optimization problem.
This is joint work with Gianni Dal Maso, Antonio DeSimone, and Luca Heltai. |
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