Mechanics of floating bodies

TL;DR

This paper develops a mathematical model for the dynamics and statics of convex floating rigid bodies in calm fluids, establishing stability criteria related to classical metacentric conditions.

Contribution

It introduces a new mechanical framework for convex floating bodies and proves stability of equilibria using Liapunov methods, extending classical equilibrium theory.

Findings

Proves stability of certain equilibrium configurations.

Establishes a mathematical foundation for convex floating bodies.

Connects stability criteria to classical metacentric conditions.

Abstract

We introduce and study the mechanical system which describes the dynamics and statics of rigid bodies of constant density floating in a calm incompressible fluid. Since much of the standard equilibrium theory, starting with Archimedes, allows bodies with vertices and edges, we assume the bodies to be convex and take care not to assume more regularity than that implied by convexity. One main result is the (Liapunoff) stability of equilibria satisfying a condition equivalent to the standard 'metacentric' criterion.