Slender Body Theory for an Oscillating Ship 



't ( f J ) 



-1 c(^) [ 



(4.1) 



The Greens function (2.18) associated with the potential cpj is written in the 

 form: 



+ G3 + G, , (4,2) 



where 



- -2 r^ j-'" A„(q,5) e ' ' '^ ' cos {e(77^-f )qsing} dq 



/^O^ ^°^^ + 27q cos5 + ^L -q 



A„(q, 5) e cos {e(77j- f)q sin 5) dq 



/Sgq^ cos2|9 + 2'yq cos d + ^l - q 



Bn(q,e) e ^^ ' ^^ cos {e(7]j-f)qsin6}dq 



^^J -/ 



-2 r"-" r 



/Sgq'^ cos^0 - 27q cos 6 + ^l ~ ^ 



(4.3) 



'"2 



With A3 = B3 = ^L 



A4 = ^oq2 cos^e + 27q cos , B^ = /S^q^ cos^^ - 27q cos 9 . (4.4) 



The term containing G^ in cpj is integrated with respect to f . The first 

 order term of cpj can easily be obtained by putting e = in the formulae with G^, 

 because all the integrals remain convergent. It is assumed that 



r F(i,od^ = r F(-i,oci^ = 



Jc ( 1 ) -^c ( - 1 ) 



The result becomes: 



221-249 O - 66 - 13 



177 



