Q = 5^ + ^1 = 2q^ [e - ig + ^^ (e - igf]^J^ 



Sn = ^? - ^2 = 2cq^ (e - ig) 



2 / n1/2 



Q-L2 = 1-|_^2 ~ ^ ^^ 



^1 "^ ^2 2 , ,1/2 . 2 , 



\ = -^rZ = 2q (e - ig) [1 + 25 (e - ig)] 



^1^2 

 Thus, the analytic solution of the complex problem is formally completed. 



(b) Real res\ilts . For practical use, real relations must now be 

 inferred from the complex relations. 



The original equations requiring real solution were Equations [2i+], 

 [25], and [26a,b,c,d]. As final resvilts, relations between v_ and e 

 and the applied force F and moment G appear to be the most useful. 



For convenience, the complex Equations [U2a,b] may be summarized 

 thus : 



^oa = (^ll-^ i^ll^ A -^ (^2 -^ ^^^2^ ^ 



%= ^^21^ ^^21^ ^-^ H2 ■'^^22^ ^ 

 the primed coefficients a' , a" , etc., being all real. Then 



- - iojt ,, .„,iajt iojt 

 V = V e = (a' + la ) Ae + (a' + la, ^j Be 



00a '11 11' '12 12 



— — i ojt / . . ,, \ . iwt / , . 11 \ ^ iwt 

 ^o = ^oa" = ^^21 * '^21^ ^^ ■" ^^22 "^ '^22^ ^^ 



Here v^ and e are the values at x = of v and 6 (or 9v/9x). 

 o o 



38 



