Multiplying out, then equating to zero separately the real and imaginary 

 parts and dividing the latter by iw, on the assumption that w ^ 0, yields 



to ml - to [mk + (I + L m) k 



+ Cg (c^ + BS) - LmBS^] + k^k^ = [Tla] 



-to^[(c^ + BS)(I + L^m) + C2m] + (c^ + BS) k^ + c^k^ = [Tib] 



The second equation can also be written 



2 (c, - BS) k^ . c^k^ 



to - , p , 



(c + BS)(I + L^m) + cm 



[Tib- ] 



In both equations all symbols denote positive quantities except that it 



may be interesting to try to make c , Cp , k, , k^ , or S zero. Hence, 



2 



Equation [71b] cannot require a negative value of to . 



2 



Equations [71a ,b] fix ui and S but, in general, an algebraic solution 



p 

 is not practical. Substituting to from [71b'] into [71a] and clearing of 



fractions gives a quartic equation in S, or a cubic if either k or k is 



zero (or both), so that the term k k disappears and Equation [71a] can be 



2 

 divided throu^ by to . The most feasible method of numerical solution 



would probably be to assume a value of S, calculate to by [71b'], and 



then calculate the value of the left member of [71a]. Successive 



approximation and interpolation would then be used in order to find the 



values of S for which Equation [71a] holds. 



The smallest positive value of S thus found will undoubtedly be a 



critical flutter speed, provided L ^ so as to couple the v and 6 motions, 



75 



