The movement of a solid in an incompressible perfect fluid as a geodesic flow (Q2884435)

The authors consider a rigid body which is surrounded by a perfect incompressible fluid filling a smooth open bounded domain in the Euclidian space. The motion of such a system is usually studied from the point of view of PDEs employing the Cauchy theory for classical solutions. By using a procedure proposed by Arnold for perfect incompressible fluids, the authors prove that the classical solutions of the above equations are geodesics on a Riemannian manifold of infinite dimension. This means that these classical solutions are the critical points of a specific action, namely of the integral over the time of the total kinetic energy of the fluid-rigid body system. The authors also prove that the motion of a rigid body in a frame attached to its center of mass can be considered as a geodesic on a orthogonal group.