ON THE SELF-DISPLACEMENT OF DEFORMABLE BODIES IN A POTENTIAL FLUID FLOW

Alexandre Munnier 1, 2
1 CORIDA - Robust control of infinite dimensional systems and applications
IECN - Institut Élie Cartan de Nancy, LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est
Abstract : Understanding fish-like locomotion as a result of internal shape changes may result in improved underwater propulsion mechanism. In this ar- ticle, 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 de- termine the equations of the inferred motion. We prove that the swimmers degrees of freedom solve a second order system of nonlinear ordinary differen- tial 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.
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Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2008, 18 (11), pp.1945-1981. 〈10.1142/S021820250800325X〉
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Alexandre Munnier. ON THE SELF-DISPLACEMENT OF DEFORMABLE BODIES IN A POTENTIAL FLUID FLOW. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2008, 18 (11), pp.1945-1981. 〈10.1142/S021820250800325X〉. 〈inria-00589796〉

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