The study of the motion of a rigid body through a fluid is considered as a general problem in the motion o rigid bodies under the action of gravity and hydrodynamic forces. This a choice of nomenclature for this field mist borrow from both rigid dynamics and fluid mechanics.
Like most problems in hydrodynamics, an exact theoretical solution of the equations of motion is available only for an idea fluid. However, as is well known, for small deviations from uniform linear motion, the equations of motion in a real fluid can linearized and solved in terms of a set of coefficients, which are determined either by theory or by experiment.
Frequently, rather than to determine the trajectory of a body, it suffices to obtain a measure of its stability. A body in a state of equilibrium is said to be stable if, when slightly disturbed from this state, it returns to it, with perhaps a slight change in position of path. Since there are various possible states of equilibrium, there are, correspondingly, various possible kinds of stability; these are defined in a subsequent section of this Bulletin.
Although the motion can be described adequately only with reference to some fixed coordinate system, it is shown in texts on dynamics that the equations of motion of a rigid body are expressed most conveniently in terms of a rectangular coordinate system moving with the body., the so-called body axes. Consequently, it has been necessary to introduce nomenclature for describing the orientation of the body axes relative to the fixed axes.