Vassilopoulos and Mandel 



Y = m(v + ru - pw) (12) 



Z = m(w+pv-qu) (13) 



K = I^p + (I,-Iy)qr (14) 



M = lyq + (I^-I,) rp (15) 



N = IJ + (ly-ix)pq- (16) 



If all other degrees of freedom except pitch and heave are now ignored from 

 Eqs. (5)-(10) and if the center of gravity is assumed to be located on the longitu- 

 dinal body axis at a distance xq from the origin of the 'TDody" axes, then, the 

 problem reduces to the examination of the coupled pitch and heave equations as 

 given by: 



ra( w - qu - Xq q) = Z (17) 



Iyq+mXQW = M. (18) 



By the same token, the equivalent set corresponding to Eqs. (11)-(16) becomes, 



m(w-qu) = Z (19) 



lyQ = M, (20) 



where the mqu term in Eq. (19) represents the main distinction between the or- 

 dinary Newtonian equation with axes fixed in space and the equation of motion 

 with axes fixed in the ship. 



Turning now to the examination of the loads, we note that in the most gen- 

 eral case, the total external force F and moment G about the center of gravity 

 must depend on: 



1. The characteristics of the body 



2. The properties of the fluid 



3. The parameters which describe the relative motion between the body 

 and the fluid. 



These may be listed as follows: 



1. Characteristics of Body 



Characteristic length (size) 



Geometry 



Mass and its distribution 



328 



