Davis and Zarnick 



I s.n ^^d^ = j 



cos i^d(, = 2-/77/2 



where 



C(iJ.) - cos ("2'^^^) "^^ ' ^^^^ ~ ^^" (t^'^^) *^^ 



Substituting the above into Eq. (A-3), yields 



{^V' 



[cos CT^] 



" " \277X/ 



For simplification, let 



Then 

 and 



w( ar) = aj cos — a^r-^ 



1 , o- 

 2 



+ ^ C (/27^xa) 



+ [sin cr^] 



I + -^ S (/2A X 0-) 



\2rm) 



4^2 



i-+ -^ C(ar) 



7T 2 2 



Sin — a'' T"' 

 2 



1+ -^ S(ar) 



For large values of a or a, going back to Eq. (A-3), we find that 



w( ar) % a 



"""2 2, •■""22 



cos -y a T'' + sin — a'' r'' 



/2acos(^a2r2-^) 



(A-4) 



g-T" 77 



T » 



(A- 5) 



REFERENCES 



1. St. Denis, M. and Pierson, W. J., "On the Motions of Ships in Confused 

 Seas," Transactions, The Society of Naval Architects and Marine Engineers, 

 Vol. 61 (1953). 



2. Stoker, J. J., "Water Waves," Inter science Publishers, Inc., New York (1957). 



540 



