A Vortex Theory for the Maneuvering Ship 



9. More General Quasi -Rectilinear Motions 



One of the reasons why we are interested in the motions parallel to the 

 (z,x) -plane of symmetry of the hull, is that they are also parallel to the vertical 

 plane. As a consequence, if we know which forces are exerted on the body in 

 forced motions parallel to the (z,x)-plane, we are able to determine the free, 

 natural motions in the vertical plane. 



Motions parallel to the horizontal plane are also of a great importance. 

 But their approach is much more complicated. 



Let us consider the equations: 



i = -(U+ a)6 + v0 + w , p 



<^ 



e + ^pd^ , 



^ 



When the motion is parallel to the horizontal plane, 1 = 0. But the components 

 normal to the (z,x)-plane of the hydrodynamic force and of the force of inertia 

 of the body do not act through the same point. Consequently, they generate a 

 f^component for the resulting moment; p and 4> cannot keep null values. Even 

 if 6 = 0, the final motion is not parallel to the (x,y) -plane, since w and q are 

 different from zero. 



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