The uses of functional analysis in ship dynamics

Abstract

Generally speaking, linear theory is unsatisfactory for the analysis of ship manoeuvres. The reason for this probably lies in the representation of fluid forces and moments, which are normally specified (on the basis of quasi-steady flow) by ‘slow motion derivatives’. Fluid forces and moments are at best represented only very crudely even though they play a dominant part in ship motions. It is known that time history effects must exist, in that the flow conditions at some instant cannot uniquely determine the flow forces and moments at that instant. Failure to allow for this is probably the major potential source of weakness in most techniques of analysing ship motion. A method is shown by which the effects of time history may be allowed for when specifying fluid force or moment. The specification, which is in terms of a Volterra series, has an approximate linear form. The standing of slow motion derivatives is examined in the light of this improved linear specification. There is no evident major obstacle to the application of the new approach to any of the branches of hydrodynamics conventionally studied in naval architecture, e. g. resistance in waves, use of the planar motion mechanism for model testing, directional stability and control (in calm water or in waves and on the surface or submerged).