A Vortex Theory for the Maneuvering Ship 

 We assume here that 



= constant . 



dt 



The angle of trim is = (O'x'.Ox). e^ is assumed to be negligible. The 

 absolute velocity of is 



Ai d^ 



V(0) . i.' ^+ ix' Tt -- iz^^ ix(u + ^)- 

 One has 



Therefore 



The drift angle is 



The angular velocity is 



^.^^y^e, U = ^, u = 0. (1) 



dt dt 



w ^ 1 d^ /o\ 



(w/U)2, (Lq/U)2 and |(w/U) (Lq/U) I are assumed to be negligible. 

 A. Steady motions 

 The steady motions here considered are defined by the conditions: 



6 - constant , -77 = . 

 dt 



Consequently, we have: 



Lq 



u ^ ■ u 



£ = rr = 



—1=0, {6 - constant = 6) . f^) 



The set of forces have the components on the axis attached to the body: 



z, X, i. 



B. Purely heaving motions 



In these motions 6 = constant. 



883 



