On the motion and collisions of rigid bodies in an ideal fluid

Jean-Gabriel Houot 1 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 : In this paper we study a coupled system of partial differential equations and ordinary differential equations. This system is a model for the 3d interactive free motion of rigid bodies immersed in an ideal fluid. Applying the least action principle of Lagrangian mechanics, we prove that the solids degrees of freedom, solve a second order system of nonlinear ordinary differential equations. Under suitable smoothness assumptions on the solids and on the fluid's domain boundaries, we prove the existence and $C^\infty$ regularity, up to a collision between solids or between a solid with the boundary of the fluid domain, of solids motion. The case of an infinite cylinder surrounded by a fluid occupying an half space, we prove that collisions with non zero relative velocity can occur.
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2006
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Soumis le : mercredi 6 septembre 2006 - 11:56:52
Dernière modification le : jeudi 11 janvier 2018 - 06:20:02
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  • HAL Id : inria-00001149, version 3

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Jean-Gabriel Houot, Alexandre Munnier. On the motion and collisions of rigid bodies in an ideal fluid. 2006. 〈inria-00001149v3〉

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