A Vortex Theory for the Maneuvering Ship 



with 



^;^o,.^,,-,.^,>.o.)-A, (w) 



(13) 



and 



^A'p;(m^,t') 



Vea; + ^ % 



da' 



5^ |sr>.*")(^)^,-(J)^ /■/>.■■ 



j' df'(^), 5r>.t ■-.■)<!.■ 



Integrating by parts the integrals in the right member of (14), we get: 



pAp,(m,,t ) . (^) 



v; + ^ %o 



-^ S7*(m,+co) +^3^ S7t('",0+) 



I* (^l 



VeA; + ^ "^0 



Bcr' L 3t'J 3t' ^i' ' ^^.^ 



This equation holds when (w/U)^, has jumps for t' >0, 

 Let us introduce now the difference 



A'S7*(m,t') = S7*(m,+co) - S7*(m,t'). 



We set 



R(m, t') = 



Vt-1 + $„„ : A §7,(11,1 ) 



(15) 



(16) 



We obtain 



R(m 



.0) = (V,i; . ^, <I>oo) 3^7 S7t(m,.c») . ^^, S7:(m,0) . 



R(m,+oo) = . 



So Eqs. (14') and (14) give respectively: 



R(m, t'-T')dT' , (17') 



221-249 O - 66 - 55 



849 



