# An alternative view on the Bateman-Luke variational principle

## TL;DR

This paper presents a new derivation of the Bernoulli equation and offers an alternative perspective on the Bateman-Luke variational principle, addressing water wave dynamics in complex moving systems and interactions with floating structures.

## Contribution

It introduces a novel derivation of the Bernoulli equation and an alternative variational principle for modeling water waves and floating structures in three dimensions.

## Key findings

- Derived boundary value problem for potential water waves in moving containers
- Formulated equations for wave-structure interactions with interior fluid sloshing
- Established nonlinear hydrodynamic equations from a second variational principle

## Abstract

A new derivation of the Bernoulli equation for water waves in three-dimensional rotating and translating coordinate systems is given. An alternative view on the Bateman-Luke variational principle is presented. The variational principle recovers the boundary value problem governing the motion of potential water waves in a container undergoing prescribed rigid-body motion in three dimensions. A mathematical theory is presented for the problem of three-dimensional interactions between potential surface waves and a floating structure with interior potential fluid sloshing. The complete set of equations of motion for the exterior gravity-driven water waves, and the exact nonlinear hydrodynamic equations of motion for the linear momentum and angular momentum of the floating structure containing fluid, are derived from a second variational principle.