Eq. (10) gives: 



A Vortex Theory for the Maneuvering Ship 



^ M'„/P,) - G(P) , (12) 



^^(Pe.t') = G(P)(-^) (13) 



Let "aj" be the case when 



= constant | for t' >0 . 



^ ^ 'o + 



In the case "a^," one has: 



7j(m,t') = y*(m,t') m , rj(77',t') . r*(T,',t') (^) , 



o + o + 



and so on. Equation (13) yields 



where r*(T]', r') = when ^' <X(t;') - Lt ', while 



is the contribution in G(P) of the area d^s = d<f' d?]' when the motion is steady, 

 say when 



t' = +00, r:;(T7',t').= r*(77',+co) = v^^i-r)'^ . 



Equation (14) takes into account the fact that Yj and consequently Wj are linear 

 and homogeneous with respect to Pj. 



Putting 



r*(T7',t') = rp^(77') F*(77',t') , [F*(T]',t') = for t' <0, F*(77',+oo) = 1] , (15) 



Eq. (14) becomes 



dT^' F*(t)',t') -— — ^ G(T,^)d<f' = G(T7^) = d77' -— — G(77^)c^' 



837 



