Mooring and Positioning of Vehicles in a Seaway 



U' = V = (119) 



where only four boundary conditions are necessary since e' can be 

 eliminated as a variable by use of Eq. (113), 



The representation of the boundary conditions at the upper 

 end of the cable (s = i), at the attachment with the buoy, shows how 

 the cable motions are influenced by the buoy motions. However, 

 the buoy motion is also influenced by the cable system dynamics 

 since a mooring force acts on the buoy as well. The mooring force 

 that affects the buoy motion is due to the component of tension at the 

 attachment point, which leads to 



X^= - T'(i) cos Ui) + To(i) sin U^^'in (120) 



Z^= - T'(i) sin ^^{i) - To(i) cos 4>o(i ) c|)' (i ) (l2l) 



M,n=-z,X„-i,Z„ (122) 



where these expressions are component terms on the right-hand 

 sides of the respective equations, e.g. Eqs. (54) - (56), With 

 T'(i,t) and 4>M-^ »t) represented as f(s)e'*^* forms the total system 

 of buoy and cable can be solved using linear equations of motion for 

 sinusoidal wave inputs at different frequencies (assuming the non- 

 linear damping terms in the buoy motion equations are linearized). 

 The "feedback" nature of the equations governing the buoy motion and 

 the cable motion is illustrated by the above discussion, where the 

 cable tension force influences the buoy motion directly and the buoy 

 motions determine the cable upper point boundary condition. 



As mentioned earlier, the study of a moored buoy system is 

 closely related to other mechanical cable system problem areas. 

 The case of a naoored ship is, of course, very similar to a moored 

 buoy but the distinguishing difference is the relative masses that 

 are Involved, For a moored ship case, the ship Is so large (rela- 

 tively) that it can be realistically assumed that only the quasi- static 

 forces applied to It by the mooring cable are significant, and that the 

 cable dynamics do not Influence the ship's response; that Is, mooring 

 cable dynamic forces can be assumed small with respect to other 

 excitation forces. Thus, the dynamic problem of the ship and the 

 cable can be treated separately. Similar reasoning applies to the 

 surface condition of a cable-towed body system. However, the 

 analysis of the component forces Involved In such systems Is appli- 

 cable to the present case of a moored buoy system, keeping In mind 

 the required coupling In the nn.athematlcal model, as shown above. 



The equations developed here for a moored buoy system have 

 to be solved In order to determine the necessary Information on 



1067 



