Wu and Whttney 
where v is an analytic function of ¢ and may involve geometric 
parameters Cy a eee Cys so that the wetted body surface corresponds 
to 7=.07, || <1, and the free surface, to = ot, ts Ceca ae 
Specific forms of the function v ({) will be given later, but our pur- 
pose at this time is merely to illustrate the type of nonlinear varia - 
tional problem that arises, 
Description of the flow is effected by giving the parametric 
expressions. f= £(6)ieand ciaf=.e 15) 
Go) n=l osilon(di/da)up= maedrad (2) 
being the logarithmic hodograph, The boundary conditions for w may 
be specified either as a Dirichlet problem, by giving 
Yr iven 
Haier, REMeACEh HAO ) (g ease , (3) 
or as a Riemann-Hilbert problem, 
6 = Im w(f +10) = 6 (é) (1 E|-n<ea)ocy bh stinaiess 
r= Re w(f +40) = 0 (fE] > 1). (4b) 
The formulation of the w problem is completed by specifying a con- 
dition at the point of infinity, say 
SLO; ( |z] > ©), (5) 
and by prescribing a set of end conditions, which are generally on 
(ey enais 
palit 1) 
iT] 
io) 
(6) 
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