Abstract. Understanding fish-like locomotion as a result of internal shape changes may result in improved underwater propulsion mechanism. In this article, we study a coupled system of partial differential equations and ordinary differential equations which models the motion of self-propelled deformable bodies (called swimmers) in an potential fluid flow. The deformations being prescribed, we apply the least action principle of Lagrangian mechanics to determine the equations of the inferred motion. We prove that the swimmers degrees of freedom solve a second order system of nonlinear ordinary differential equations. Under suitable smoothness assumptions on the fluid’s domain boundary and on the given deformations, we prove the existence and regularity of the bodies rigid motions, up to a collision between two swimmers or between a swimmer with the boundary of the fluid. Then we compute explicitly the Euler-Lagrange equations in terms of the geometric data of the bodies and of the value of the fluid’s harmonic potential on the boundary of the fluid. 1.

learning and transfer of spatio-temporal movement characteristics, ” Int.

Summary: Reinforcement learning has proven successful at harnessing the passive dynamics of underactuated systems to achieve least energy solutions. However, coupled fluid-structural models are too computationally intensive for in-the-loop control in viscous flow regimes. My vertically falling soap film will provide a reconfigurable experimental environment for machine learning controllers. The real-time position and velocity data will be collected with a High Speed Video system, illuminated by a Low Pressure Sodium Lamp. Approximating lines of interference within the soap film to known pressure variations, controllers will shape downstream flow to desired conditions.

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In this paper we study the locomotion of a shape-changing body in a twodimensional perfect fluid of infinite extent with potential flow. The body is assumed to be neutrally buoyant (its density is set for the upthrust to be null and we neglect the torque effects of the buoyancy force). The shape-changes are prescribed as functions of time satisfying constraints ensuring that they result from the work of internal forces and torques only: conditions necessary for the locomotion to be termed self-propelled. The net rigid motion of the body results from the exchange of momentum between its shape-changes and the surrounding fluid. The aim of this paper is several folds: First, it contains a rigorous framework for the study of locomotion in fluid by shape-changes. Our model differs from previous ones in that the number of degrees of freedom related to the shape-changes is infinite. The Euler-Lagrange equations of motion are classically obtained by applying the least action principle to the system body-fluid.