Minimum Wave Resistance of Surface Pressure Distribution 



and since 



then 



P.i(x,y,0) = J^ ^K2„(y/2) J^^Cx) , 



P.5(x,y,0) = _^P_j(x,y,0) 



ox 



(34) 



P.5(0,y.O) . -Ko(y/2)- TTK2(y/2) = -j U " 2 _ K„(y/2) 



16 



16 



dy- 



(35) 



To solve the integral equation (33), assume the next expansion in Mathieu 

 functions (15) 



H(y) = 0(0)/sin e , y = cos 5 



CD 



Then, since there is the integral 



^ f ^0 (I '''°' ^ " ''°' ^'') ^^2n(^''-q) d^' = ^2n ^e^^C^.-q) 



where 



because of the representations 



( 2n) 



ce2„(0,q) 



Fek,„(0.-q) 

 ce2„(0,-q) ' 



r'" 



— cos (2k cos 9 sinh u) cej^C^.-q) d^ = 

 Jo 



-co 



— I cos (2k cosh z sinh u) Ce2n(u, q) du = 



and the relation 



( 2n) 

 (-1)" Aq Ce2„(u.q) 



ce2„(0,q) 



(-1)" Aq'"' Fek2„(z,-q) 

 ce2„(0,q) 



Fek2„(0,-q) 

 Re [Fek2.(-i^,-q)] = .^^^^^.^^ ce2„(^.-q) . 



(36a) 



(36b) 



(37) 



(38) 



(39a) 



(39b) 



(40) 



783 



