A New Appraisal of Strip Theory 



For reasons of consistency and systemization in future analyses, we herein 

 suggest the use of and shall adhere to the nomenclature of Bulletin No. 1-5 of 

 SNAME [25]. Following the above definitions it is shown in Refs. [12,26,27] that 

 in order to obtain separate vector force and moment equations, the principles of 

 linear and angular momentum must be used for the center of gravity of the ship, 

 but must be measured relative to the 'TDOdy" axes fixed about the point defined 

 previously. If we therefore denote by F the total external force and by G the 

 total moment of the external forces about the center of gravity, then, the princi- 

 ples of linear and angular momentum give, 



F = ^(mUo) (1) 



and 



G = ^ (Hg) . (2) 



where 



F = 1 X + J Y + k Z , (3) 



G=iK+jM+kN. (4) 



Following the principles of dynamics and carrying out the operations indicated 

 above, it may be shown [26] that the complete six-degree of freedom motion of 

 the ship is characterized by: 



X = m [u+ qw- rv- XQ(q2+ r^) + yQ(pq- f) + ZQ(pr + q)] (5) 



Y = m [v +ru-pw- YqCt^ + p^) + z^Cqr - p) + XQ(qp + f)] (6) 



Z = m [w +pv -qu - Zq(p2+ q2) + Xq ( rp - q) + YcCrq + p)] (7) 



K = I^p + (I^ -ly) qr + m [yQ(w + pv - qu) - Zq(v +ru- pw)] (8) 



M = Iyq+(I^-Ij,)rp+m [zq(u + qw - rv) - Xq(W+pv - qu)] (9) 



N = I^ r + (ly-I^)pq + m [xq(v + ru -pw) - y^fu +qw- rv)] (10) 



where the various symbols are defined in Ref. [25]. From this general approach, 

 it may be seen that if G , the center of gravity, is identified with the origin of 

 the "body" axes, then the above equations reduce to the well known Euler equa- 

 tions: 



X=m(u + qw-rv) (11) 



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