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

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 two solids or between a solid with the boundary of the fluid domain, of the solids motion. The case of an infinite cylinder surrounded by a fluid occupying an half space is tackled. By a careful asymptotic analysis of a Neumann PDE, when the distance between the cylinder and the wall goes to zero, we prove that collisions with non zero relative velocity can occur.
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Cited literature [15 references]

https://hal.archives-ouvertes.fr/hal-00095617
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Submitted on : Monday, September 18, 2006 - 2:44:51 PM
Last modification on : Saturday, June 25, 2022 - 7:44:52 PM
Long-term archiving on: : Friday, May 13, 2011 - 11:52:58 PM

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• HAL Id : hal-00095617, version 1

### Citation

Jean-Gabriel Houot, Alexandre Munnier. On the motion and collisions of rigid bodies in an ideal fluid. Asymptotic Analysis, IOS Press, 2008, 56 (3-4), pp.125-158. ⟨hal-00095617⟩

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