-Ztt 

 M* = - I I p*(z - Zq) cos e R de dz 



- -in - u 



.0 



-LI 



= -^<^pK^lj (z - z^)S(z)e^^dzj [44] 



(j [e +4^(Zi- z^)] e^^lS(z^)dzjj 



or in terms of the integrals Pi , P^' Qq' ^^"^ ^1" 



fJ = -ia;pKi[K ^ Qo(K)- S(0)]2 

 , wm K . , ,2 



= -i — rr ^ t^ -Qo(K)xKH]^ 



[45] 



2 

 F* = -i ^ K3Qo(K)[eQo(K) + 4iQl(K)] [46] 



My = ~ 2 ^ K^Qi(K)[|Qo{K) + 4;Q^(K)] [47] 



In place of Equations [31], [32], and [33], we obtain the damped equa- 

 tions of motion 



2| + P, 4; = - 2AQq{K) cos ut 



, . [48] 



+ ^ ^ K^Qo(K) [eQo{K) + 4^Qi(K)] 



(1-XKH)^ = A sinojt [1 -XKH Qq(K)] 



,2 [49] 



+ i — -^ [1 -Qo(K)XKH]' 

 a)p ;j.2j^2 



^(P2 - Pj/K + k^) + Pj ^ = - 2A Qj(K) cos wt 



[50] 

 + i^ K^Ql(K)[eQo(K)+ 4;Qi(K)] 



16 



