A Vortex Theory for the Maneuvering Ship 



"^ L JJ i^ Sy;(m,t') n(m) dS(m) I . 



Consequently, in the quasi-steady motion, we have a general resultant: 



(23) 



The difference between this resultant and the resultant in the real motion is 



A?;(t') . n,[l)^, -?;(t'). 

 One has 



where 



Moreover: 



A5;(t') = -f[^'\t') + A'j;(t') 



?l^'\t') = -P^^ (5),, if ^i^"^'0+) nC"^) dS(m) 



^0 1 



(fL /J 3P 8^;(»'t') n(m')dS(m) 



" s 



Let ZJ(t'), Zg j(w/U)^, be the components on the z-axis of the forces above. We 

 put: 



+ PT 



z- ^ 



1 \U/,, 



\ pAU^a 



1 (S),, 



(24) 



853 



