A variational principle for three-dimensional interactions between water waves and a floating rigid body with interior fluid motion

Abstract

A variational principle is given for the motion of a rigid body dynamically coupled to its interior fluid sloshing in three-dimensional rotating and translating coordinates. The fluid is assumed to be inviscid and incompressible. The Euler–Poincaré reduction framework of rigid body dynamics is adapted to derive the coupled partial differential equations for the angular momentum and linear momentum of the rigid body and for the motion of the interior fluid relative to the body coordinate system attached to the moving rigid body. The variational principle is extended to the problem of interactions between gravity-driven potential flow water waves and a freely floating rigid body dynamically coupled to its interior fluid motion in three dimensions.