Mooring and Positioning of Vehicles in a Seaway 





'12 



'22 



32 



Y 



N 



K + (OG)Y 



(30) 



■where the matrix here is also symraetric, i.e. bjg = ^21' ^13 ~ ^3i» 

 bgj = bj2' The elements are defined by 



b|| = - (^m + \ A22 ^i) ^ + iwCyNy + k^ 



b,3 = b3, = - u) 



A,, e de + iwN, 



^12 - ^2, = - 0) 1 -"22^ "^ "^ iWlNy^ 



\ (A42 + (OG)A22) d4 + icoCyNylBG 

 ^22 = - (I2 ■*■ 3 ^^22^^ d|) co^ + icoC^N^ + k^ 



^ J (A42 + (OG) A2'2) i dl + iwNy^^l BG | 



^23 = ^32 = 



33 = - ui\ + icoN^ + W I GM I 



b,, = 



(31) 

 (32) 

 (33) 

 (34) 

 (35) 

 (36) 



The presence of symmetric matrices helps in effecting an 

 easier solution of the equations, obtained by matrix inversion on a 

 large digital computer. The solutions are then available for each 

 degree of freedom and also for any linear combination of degrees of 

 freedom. The real form of the final solutions is obtaine-d by taking 

 the real part of the complex function, which was the original defini- 

 tion implied in the complex representation of the solution variables. 



The lowering line dlsplacemients are related kinematically to 

 the body motions, and hence they are relatively simple to determine 

 once the different methods of lowering loads are specified in this 

 study, viz. center-lowered loads and boom-lowered loads. Center- 

 lowered loads, as the name indicates, are lowered through some 

 sort of opening through the ship's keel, and it is assumed that this 

 is done at just about annidships. The instantaneous displacement 

 vector components of the load and lowering line are Sj^, s and s^ 

 and are then given by simple geometry as 



1033 



