Alternative approach to explore the stability of floating bodies

Abstract

We present a simplified model of a boat to study its rotational dynamics, which is a significant criterion for the development of navigation systems. The stability of a floating body can be examined by means of rotational potential energy, which depends solely on the boat’s gravity center and a point called the metacentric height. Typically, this geometric point is a function of the body’s orientation in relation to the fluid surface, and the estimation of its value can often be ambiguous. This paper presents an alternative method for calculating the metacentric height using a vectorial approach, as well as a general definition of rotational potential energy applicable to this type of problem. The potential energy facilitates the determination of stable and unstable equilibrium directions as a function of the boat’s relative density and orientation.