SINGULAR PERTURBATION PROBLEMS IN 

 SHIP HYDRODYNAMICS 



T. Francis Ogilvie 



University of Michigan 

 Ann ArboVy Michigan 



NOTATION 



ajj added-mass coefficient 



bjj damping coefficient 



b{x,z) hull offset 



Cjj restoring-force coefficient 



C(x) contour of body in the cross section at x 



Fj (t) force in j-th mode due to body motion 



F: (t) force in j-th mode due to incident waves 



g gravity constant 



g(x,z;c) Y offset of camber surface 



G(x,z) g(x,z;€)/€ 



h(x,z;c) half- thickness of body (equal to b(x,z) for a symmetri- 



cal body) 



H(x,z) h(x,z;c)/c 



H(x) part of free- surface deflection in problems in two 



dimensions (see Eq. (5-15)) 



H projection of a body onto the y = plane (the center- 



plane of a ship) 



I 7:1 



j j k unit vectors parallel to three Cartesian axes 



ki m Fourier-transform variables corresponding to x, y, z 



respectively 



K„(z) modified Bessel function of second kind 



L length of a ship, or the segment of the x axis between 



bow and stern cross sections 



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