Kaplan, Sargent and Goodman 
of various study contracts, viz. the Office of Naval 
Research, the Naval Ship Research and Development 
Center, and the Surface Effect Ships Project Office. 
INTRODUCTION 
In order to predict the dynamic performance of various naval 
vessels, different methods of simulation are often employed. The 
general term ''dynamic performance" used here refers to the deter- 
mination of dynamic stability, maneuvering and turning properties, 
response to control input commands, motions in wave systems, etc; 
the term ''simulation"' includes both free model trajectory tests as 
well as the use of computer solutions based on a mathematical model 
that is assumed to represent the craft motions. Considering the basic 
limits of free model testing, which are associated with limitations in 
the size of models and/or test facilities (or inherent limits such as 
in the case of submarine maneuvers), propulsion and control model- 
ing errors, time constant differences, etc., the major emphasis for 
motion prediction is the use of computer simulation using mathema- 
tical models. 
When considering prediction and simulation studies of ship 
dynamics with the use of a mathematical model, a vital aspect is es- 
tablishment of the proper form of the equations as well as the appro- 
priate numerical values of the various parameters (coefficients, 
stability derivatives, etc.) entering the equation system. At the 
present time the main method of determining the various hydrody- 
namic force and moment coefficients in a desired mathematical model 
for a particular type of marine craft is by means of captive model 
tests in a towing tank, together with the associated mathematical 
analysis of the experimental data in order to provide the required 
coefficients, Various special purpose apparatus exist. 
GENERAL DESCRIPTION OF ANALYTICAL TECHNIQUES 
When considering a vehicle in an undisturbed smooth water 
environment, transient responses of the craft are excited by means 
of different initial conditions or excitation inputs (such as a rapid 
rudder deflection or other impulsive disturbance). The measured 
outputs (i.e. vehicle motions) are recorded and operated upon by a 
technique that is essentially a generalization of a Newtonian iteration 
procedure [3] . The differential equations of motion of the vehicle, 
whether itis linear or nonlinear, are used together with additional 
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