When a rigid body departs from a uniform motion in a fluid, it is usual to assume that the forces and moments exerted on the body at any instant by the fluid are determined by the motion at that instant. This is the assumption of "quasi-steady flow" and it is on this basis that the fluid forces and moments are represented. Although this approach often suffices for aircraft it is known to be quite inadequate for ships, with the result that complicated and diverse non-linear fluid representations have been devised.
It has recently been found, however [1,2], that an unambiguous representation of the fluid forces and moments on a ship can be formulated in terms of Volterra series. This theory allows the assumption of quasi-steady flow to be relaxed and also has a simple approximate form. The latter does not destroy the linearity of the representation with which fluid forces and moments may be specified whilst the ship performs a non-steady motion. This fresh linear theory, which may well supplant the semi-empirical non-linear theories in current use, is explained and developed in simple terms. In particular, compatible definitions of "fluid derivatives" and "oscillatory coefficients" are presented.