Understanding and Prediction of Ship Motions 



E[^ ■\^\ -vlvl 



2-/< 



2-/%^ 



yi - p^ X 3p + 2( 1 + 2p^) tan" 



\/l + P - VI- P 



Vi + p + Vi- P 



[4p 



4^^^^-^-8i-' ••■] 



? V ^v^ ' 3 a^o- f ^ 157T „ 3„ 3 ?^^ 



(3.14) 



where 



P = 



'iv 





From these results and the relations 





(3.15) 

 (3.16) 



the result is 



(^) 



o '^ o ' o ' 



i^ [ e"^'^^^''-^^ E[<^„(t + r)4jM)- l0o(M)l] dr 



R . (t) e'^"^ dr 



,2~ f2~ 



(3.17) 



Accordingly the 2nd term of the Eq. (3.10) is 



2H[/SWJ^] S (a;) = 2 y^a. /3S^ ^ (co) R {- jo; Hg(a.)} 



o ^ o I '^ o 



where 



q ro;) = Q{HJa))} 



2 i/— o- . /3 S , . ( oj) X ojq J w) , 



2aaj 



(a;2- c^2>)2 ^ 4^2 ^2 



(3.18) 



(3.19) 



119 



