The movement of a solid in an incompressible perfect fluid as a geodesic flow

Abstract

The motion of a rigid body immersed in an incompressible perfect fluid which occupies a three- dimensional bounded domain have been recently studied under its PDE formulation. In particular classical solutions have been shown to exist locally in time. In this note, following the celebrated result of Arnold concerning the case of a perfect incompressible fluid alone, we prove that these classical solutions are the geodesics of a Riemannian manifold of infinite dimension, in the sense that they are the critical points of an action, which is the integral over time of the total kinetic energy of the fluid-rigid body system.

References in corpus (2)

• The Geometry and Dynamics of Interacting Rigid Bodies and Point Vortices
• The Dynamics of a Rigid Body in Potential Flow with Circulation

Cited by in corpus (6)

• Uniqueness results for weak solutions of two-dimensional fluid-solid systems
• Point vortex dynamics as zero-radius limit of the motion of a rigid body in an irrotational fluid
• Energetic decomposition of Distributed Systems with Moving Material Domains: the port-Hamiltonian model of Fluid-Structure Interaction
• External boundary control of the motion of a rigid body immersed in a perfect two-dimensional fluid
• Motion of a particle immersed in a two dimensional incompressible perfect fluid and point vortex dynamics
• On the "viscous incompressible fluid + rigid body" system with Navier conditions