Testing Ship Models in Transient Waves 

 2^ J 



w(t) 



j W I W I X/ g JOJT 



e^'^^dw. 



(A-1) 



Expanding into trigonometric terms and noting the symmetrical properties 

 of the function, we have after simplification 



w(r) = — cos (-o)^ x/g + orr) dco - — cos (o)'^ x/g - orr) dw 

 ^' \ 



Employing the technique used by Lamb [7] we let 



(A-2) 



g-^ 



1/2 \ 2x 



and 



2x" 



These terms are substituted into Eq. (A-2), yielding 



1 g!^ f" 



77 ^1/2 J 



COS (^2 _^2^) j^ 



.1/2 



I CO 



CO 



I cos 



S (^2_^2) d^ + COS (^2_ ^2>) d^ 



o 



f COS ^2d^ + j 



COS ^2 j^ + COS ^-^ d^ 







00 



r sin ^2d^ + r sin ^2^^ 



_ - a 



We can make the following identification: 



r cos ^2d^ = I COS ^2d^ , ^ y^^ Q^-) . 

 o- 



I sin ^2dC = r sin ^2d^ = rr \/^^ C(m) ; 



J J. \cr\ 



(A-3) 



539 



