TABLE OF CONTENTS In this text we will consider the ship to be a "rigid body", that is, it is "composed of a continuous distribution of particles having mutual distances that are inextensible" (Shames [1961]). While all ships undergo elastic and possibly plastic deformations, these are of much smaller magnitude than displacements of interest in maneuvering and seakeeping studies and thus can safely be neglected in such work.
Two general types of coordinate systems will be useful in the following discussions: fixed systems (relative to the earth) and moving systems, which usually have at least one axis fixed with respect to the moving body. Right-handed Cartesian coordinates ?, ?, ? will be taken to be fixed with ? and ? lying in a horizontal plane and ? vertical, positive downward. The latter may seem a bit strange, but it is consistent with the convention for body-fixed axes in maneuvering in which x is the longitudinal coordinate, positive forward; y is the transverse coordinate, positive to starboard; and (by process of elimination) z is "vertical" and the positive sense must be "downward" in a right-handed system. Most marine craft have a transverse plane of symmetry and the origin of this "body" coordinate system is generally taken to lie in that plane. The longitudinal location of the origin is sometimes chosen to be at amidships and sometimes at the LCG; for the moment it will be assumed to be arbitrary. It is convenient, for...
