„2 T 1 



Pn = - p u \-zr + 



8x 2 ' Y 0' 



j oy, "Tj "Vj_ 



Pi = " P \ ~KT~ + u "5 +v "5 +w "5 — 



1 * dt dx dy dz 



(317) 



On integrating the pressure over the moving hull surface, a periodical 

 term comes from the integration of p- because of the periodical variation 

 of the hull surface. We regard this as a correction to the restoring 

 forces due to the forward motion. Forces and moments due to the period- 

 ical potential are given by 



\ = PjJ n^cfrj+yV^) 



dS 



(318) 



where S is the hull surface at the average position and 



♦ 1 = a^/at 



APPENDIX B - THEOREM OF TUCK AND RELATIONS 

 DERIVED THEREFROM 



Tuck has proved a theorem with respect to the integral in Equation 



(318) as follows 



Tuck 1 s Theorem 



If ij) is a harmonic function defined in the lower half space outside 

 the surface S_ which has a vertical tangent at z = 0, and V = (u,v,w) is 

 the velocity of an irrotational motion, which satisfies the boundary 

 condition 



un 1 + vn ? + wn = 



(319) 



on S , the following relation is valid. 



J [m.<J>+n.(V« 



V<j>)] dS = - 



n.tj)wds 



(320) 



111 



