Thus, the restoration forces can be linear or non-linear, 

 but, the important point is that given the instantaneous dis- 

 placements, these forces can be determined. Also, for ship- 

 dominated systems, a quasi-static treatment has been customary 

 on the assumption that the system inertia is very large relative 

 to the restoration forces. For cable-dominated systems, this may 

 be no longer true and in these cases, it becomes necessary to 

 consider the cable dynamics. It develops that this division 

 constitutes one of model hierarchy characteristics (e.g., static 

 or dynamic with respect to cable forces). 



The time-varying excitation term can be linear or non-linear 

 in the sense that they are non-linear with respect to amplitude 

 or surface elevation. The non-linearities are attributable to 

 two different sources but for the same reason. For example, they 

 can result from monochromatic higher-order waves, or from frequency 

 interactions between components of wave spectra. Solution of 

 the free surface boundary value problem carried to second order 

 in either case will disclose these non-linear occurrences. 



In summary, the mooring dynamic model described by Equation 

 (1), although 'linear' in one sense (i.e., the integral term), 

 is suitable for handling non-linearities which occur in the 

 other terms. It should be emphasized that this is a deterministic 

 model and therefore will not yield the response statistics directly. 

 Also, although the model is consistent for first order solutions, 

 there is somewhat of an inconsistency in utilizing the model for 

 higher order solutions. This will be illustrated in the next 

 section . 



As a final remark, all other time domain deterministic models 

 can be shown to be subsets and/or special cases of the model des- 

 cribed above. This includes any model having less than six (6) 

 degrees of freedom, any model in which the modes are uncoupled, 

 any model in which the mooring forces are linearized or any 

 model in which the excitations are approximated by any simplifying 

 assumption (e.g., slender body assumption leading to strip theory). 



19 



