ship Maneuvering in Deep and Confined Waters 



If the body has a plane of symmetry there remain 12 different 

 acceleration derivatives , and for a body of revolution generated 

 around the x axis there are only the three derivatives A , A^„ and 



The motion of the Ideal liquid takes place In response to the 

 force and nnoment expended by the moving solid. At any time this 

 motion may be considered to have been generated Instantaneously 

 from rest by the application of a certain Impuls wrench. The rate 

 of change — cf.Eq, (4,5) — of the Impulse wrench is equal to the 

 force wrench searched for. Again, the work done by the Impulse Is 

 equal to the Increase of kinetic energy, and as shown by Milne - 

 Thonnson [13] the force and moment on the body may therefore be 

 expressed In terms of the kinetic energy of the liquid, 





5 = d (^\ . X i4 - V X :^ 



(5.4) 



"at 





an an av 



(The partial derivations shall be considered as gradient operators.) 

 The complete formal expressions for the Inertia forces In the Ideal 

 fluid have been derived from Eqs. (5.3) and (5.4) by Imlay [ 14] , and 

 they are here given In Eq, (5, 5), 



Xj^ = Xj^u + X^(w + uq) + X.q + Z^wq + Z. q^ + X-v + X^ + X^r 



- Y^vr - Y^rp - Y^r^ - X^ur - Y^wr + Y^vq + Zj^q - (Y- - Z^)qr 



Yj^ = X.u + Y^w + Y.4 + Y^v + Y^p + Y^^ + X^vr - Y^vp + X-r^ 



+ (X- - Z.)rp - Z^2 - X^(up - wr) + X^^ur - Z^wp - Z-pq + X.qr 



^id = X^(u- wq) + Z^w + Z.4 - X^uq - X-q^ + Y-^ + Zj^ + Z-r + Y;vp 

 + Y. rp + Y.p^ + X.up + Y^wp - X;,vq - (X^ - Y^)pq - X^qr 



829 



