Ogilvie 



mj (j = 1 , . . . , 6) a set of functions defined over the sur- 



face of a slender body (see (2-75)) 



in(x) added mass per unit length of a slender body 



ni (j = 1 , , • . , 6) a set of functions defined over the surface 



of a slender body, equal to the components of the unit 

 normal vector for j = 1, Z, 3 (see (2-72)) 



n.(x) damping coefficient per unit length of a slender ship 



n unit vector normal to body surface (usually taken positive 



into the body) 



N unit vector in a plane x = constant, normal to body 



contour in that cross section 



p pressure 



r radius coordinate in cylindrical coordinate system 



rQ(x,9) radius coordinate of a slender body 



r xi + yj + zk 



s half-span of a horseshoe vortex or a lifting line 



s(x) local half-span in wing cross section at x, or cross 



section area of a slender body (taken as the cross section 

 area of the submerged part, for a ship) 



5 half- span of a wing of large aspect ratio 



T(x) keel depth of a ship at cross section at x 



T-. transfer functions between motion variables and forces 



on body 



U speed of a body, or speed of an incident stream (the 



latter invariably being taken in the positive x direction) 



v(x,y,z) fluid velocity at (x,y,z) with uniformi stream at infinity, 

 U = 1 , flowing around a body 



X y z Cartesian coordinates 



X Y Z stretched Cartesian coordinates, e»g,, x = X, y = eY, 



z = eZ for a slender -body problem, xyz being far- 

 field coordinates , XYZ near-field 



Zn(x,y;c) terms in a near-field expansion of t,(x,y;e) (cf. 

 ^n^x,y;€)) 



a„(x,z;€) (^„(x,0,z;c) in thin -body problem 



•y (x,z;c) normal velocity component in the plane of a sheet of 

 dipoles 



6 motion- amplitude parameter in ship-motion problems 

 C small paramieter in most problems considered 

 C,(x,y,t) displacement of the free surface 



664 



