Application of Kirchhoff’s equations of motion to the dynamically coupled system of a rigid body with a completely-liquid-filled cavity

Abstract

This paper considers the dynamical problem of a rigid body with a cavity that is completely filled by a liquid. The dynamically coupled motion of the rigid body and the liquid is examined in the absence of any external forces or torques. This problem is not new, but the paper draws attention to the fact that Kirchhoff’s equation of motion, which was derived for the dynamically coupled motion of a homogeneous rigid body fully immersed in a liquid, applies to this problem as well. The methodology is explained. Details of a simple, idealized planar example, in which a vorticity field in the form of a single point vortex is also added to the fluid flow field, are presented. In principle, this simple model could be extended to an elastodynamic model to study the dynamically coupled motion of an elastic body and a cavity completely filled with liquid in the framework of linear elasticity.