On the use of Equilibrium Axes and Body Axes in the Dynamics of a Rigid Ship

Although it is natural and usual to employ body axis in the theory of ship manoeuvring and directional stability, the motions concerned are performed in the ‘rigid body modes’ of hydroelasticity theory and the theory of seakeeping, in which equilibrium axes are used. The dynamics of a rigid ship can therefore be approached from two standpoints. The theory of body axes is summarized and the less familiar theory of equilibrium axes is developed in a simple way from first principles. The two approaches are then compared. The transformations that are needed to adapt hydrodynamic data for use with the two types of axes are examined. These are of considerable practical importance in view of the present scarcity of data.