The Hamilton-Kelvin and Hamilton-Dirichlet Principles Associated with Motions of a Floating Body in Waves

Abstract

The estimation of motions of a floating body in waves is one of the most important problems to assure the safety of ships and various marine structures, and much study has been done using various methods. This paper discusses this problem from the viewpoint of the Hamilton principles in mechanics. In case of a steady irrotational flow of an incomplessible and invicid fluid, there exist variational principles called as the Kelvin and Dirichlet principles. The existence of the similar principles can be shown for water wave problems. In this paper, not only the fluid motion but also the motion and elastic deformation of a floating body are covered within the variational principles, and mechanical system consisting of a floating body and a fluid is discussed in a unified manner.