In the expressions for $' and p '\ several terms which are of higher 

 order in small variables have been omitted. 



The forces and moments due to this pressure distribution are calcu- 

 lated from Equations [ 12a] through [I2f], with asterisks inserted where 

 appropriate. The results are as follows: 



Xf = - ipcuk^|(iQ-<^ao sine.)T^ + PT^T^j 



Yf = -|pc^k^|(yQ + ^aQ cos e.)T^- c^T^tJ 



Z* = - |pGok/zQ+aQ(a sine. - p cos e.)\[S(0)- kT^]^ 



A* = - I pcokaQ sin 9. | Zq + a^ ( a sin 9. - P cos 9.)y [S(0) - kT^] 

 + I pcok^jc^Q + VaQ cos e.)TQTj - ^tJ| 



B* = ^ pwkaQ cos 9. I Zq + aQ(Q' sin 9. - |3 cos 9.)j. [S(0) - kT^] 

 -ipwk |(iQ - -^aQ sin e.)TQT^ + pTj )■ 



There is no need for a damping moment F- , since the ■y-motion has no 



resonance in any case. 



N 

 The modified equations of motion are obtained by adding J_, X''", 



i = l 

 etc., to the right-hand sides of the previous equations, [I5a] through 



[l5f], or alternatively, to [l6a] through [ 1 6f ] . After simplification, 



the equations become, for N > 2, 



N |[2(M + Mq/N)^^ + ipook^T^iQ] + [pS^p + Ipo^k^TpTj P]j 



N [l^^l 



= 2 pgkAT^ y cos (kaQ cos 9. - cot) 



i=l 



24 



