Similarly, for the surface integral in Equation [8] , 

 Up [c. cos Cn,C) - C cos (n,c)] dS 



= 111 [pQE.^ - 2 iw^p AC exp (- Kh + iK? cos 6 - icot) 



+ Pg 5] dV [20] 



= r S(C) [pes - 2 ioj p A? exp (- Kh + iKC cos 6 - iwt) 

 + Pg €] d5 



Substituting Equations [19] and [20] in the motion Equations [7] 

 and [8] , we obtain 



m^ + (T/c) Cq - CT£/c)e 



= pg KA cos e exp C-Kh - itot) / S(5) exp (iK^ cos g) d5 [21] 



6(1 + p r 8(5)5^ dC) + T£ (1 + £/c) 6 - (T«,/c) 5^ 



- Mg C^^ e = 2 ipg KA exp (- Kh - iwt) [22] 



/ 



S(C) C exp (iK5 cos 6) d^ 



where in Equation [22] we have used the equilibrium condition Equation [1] 

 and the fact that 



Js 8(5) d? = V 5(.g 



to cancel the nonos dilatory terms. 



Equations [21] and [22] are coupled equations of motion for the 

 surge and pitch motions of the body. Two simplifications can be made. 

 First, if the body length is small compared to the wavelength, the ex- 

 ponential 



ik^ cos g ^ T 



