is usually necessary to formulate the problem in such a way that 

 the nonlinear effects thought to be of importance to the phenomenon 

 of interest are included, and other, less important quantities are 

 represented only approximately. It is clear that such an approach 

 depends heavily on the insight and experience of the analyst for 

 its success. Model experiments and full scale observation of 

 similar structures may contribute much to the understanding 

 required for the formulation of this approach. 



II. THE EQUATIONS OF MOTION 



The general procedure followed in analyzing the dynamic response 

 of a floating platform to waves is based upon the assumption that 

 it behaves as a rigid body having six degrees of motion freedom, 

 and that any effects of the elastic deformation of the platform 

 are negligible. The external forces acting on the platform in- 

 clude those which result from the relative motion with respect to 

 the water, those exerted by the mooring or positioning system and 

 other external effects such as wind. 



In deriving the equations of motion, it is first necessary to 

 define two coordinate systems which are shown in Figure 1. The 

 first is labelled OXYZ and is assumed fixed in the platform with 

 its origin located at the center of gravity. The second, oxyz, 

 is fixed in space and its location is defined with some reference 

 to the first system. For example, if we are analyzing the wave- 

 induced oscillatory motion of the platform about its mean position 

 it may be convenient to define the space coordinate system in such 

 a way that it occupies the mean position of the platform system. 

 In the case that there is no mean position of the platform, the 

 space coordinate system might coincide with the initial position 

 of the platform system. In general, the equations of motion are 

 formulated in such a way as to describe the time-varying position 

 of one coordinate system with respect to the other. 



The complete equations of motion are given in the Appendix 

 where it is noted that the equations of rotational motion contain 

 nonlinear terms involving products of the angular velocities and 

 trigonometric functions of the angles which relate the position 



127 



