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We consider the motion of several rigid bodies immersed in a two-dimensionalincompress-ible perfect fluid, the whole system being bounded by an externalimpermeable fixed boundary. The fluid motion is described by the incompressibleEuler equations and the motion of the rigid bodies is given by Newton's lawswith forces due to the fluid pressure. We prove that, for smooth solutions,Newton's equations can be recast as a second-order ODE for the degrees offreedom of the rigid bodies with coefficients depending on the fluid vorticityand on the circulations around the bodies, but not anymore on the fluidpressure. This reformulation highlights geodesic aspects linked to the addedmass effect, gyroscopic features generalizing the Kutta-Joukowski-type liftforce, including body-body interactions through the potential flows induced bythe bodies' motions, body-body interactions through the irrotational flowsinduced by the bodies' circulations, and interactions between the bodies andthe fluid vorticity.

Dynamics of rigid bodies in a two dimensional incompressible perfect fluid