Ship Waves and Wave Resistance 



For evaluation of Eqs. (29) and (31) we have to keep in mind that for v- the 

 Green's function G has a representation for ^ >> X as a system of free waves 

 like 



00 



^x - /_, gv COS 



V =- CO 



W.7o(X-^) 



K^^o(Z+0 



cos (U^7oY) 



(32) 



with g^ - g_^ = -87tk^7o/(M^T) (see the appendix) and that we have 



(33) 



and 



W 



(34) 



Therefore 



W 



(35) 



(36) 



Air=i^jj^(^.o 



2^7o J_^ 



0x'^W^7o sin (W^7o^) + ^z'^K^y cos (W^7o^) 



( 1) 



d^d^ 



and 



F(^,0) ^xx sin (W^7o^) d^, 



4'^Wv^o c°s (W^7o^) - ^z'^K^7o sin (W^7o^) 



(37) 



w 

 - ^^ r F(^,0) V'xi^ cos (W^7o^) d^ 



d^d^ 



(38) 



661 



