Wu and Whttney 
I [ ar 2 ] is now an ordinary function of the Fourier coefficients 
Te : 
Tv 
Roa(ele Boke. e~) = fee 8.5 cos Osc c )sin6 dé 
1 n m 1 
fo) 
SC sb ea Sy SEY (32) 
For I to be extremum, we require that 
d1/ O Fee = 0) (lz eyok, ma) ; (33) 
and 
a1 / dc, =(7*¢ Giger ie LOPE (34) 
These (m+n) equations together with M constraint equations (12) 
determine the m coefficients Yor Ym? " parameters c,... 
Cy, and M multipliers \, ,... M.- It should be pointed out, 
however, that the coefficients y;'s and parameters cj's generally 
appear in the expression for I(y,,c;) in a nonlinear or transcendent- 
al form, making their determination, by algebraic, numerical means 
or otherwise, extremely difficult even when their number is moderate- 
ly small, such as three or more. 
The preceding general theory will be further discussed and 
clarified with several specific examples in the presentation of this 
study. 
ACKNOW LEDGMENT 
This work was sponsored in an early stage by the Naval Ship 
System Command General Hydrodynamics Research Program, ad- 
ministered by the Naval Ship Research and Development Center under 
Contract Nonr-220(51), and partially by the Office of Naval Research, 
under Contract N00014-67-A-0094-0012. 
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