and it follows that 



M C + (T/c)C - (T£/c)e = pg KA V cos g exp (-Kh - icot) [23] 



(I + pJscaC^ dO + T£ (1 + £/c)e - CT£/c) g^ 

 - Mg C(.(, = 2 ipg KA V5^g exp (- Kh - iwt) 



[24] 



In this form the only integral involved is the geometric quantity 



I' = p r SCOC^ d? [25] 



(i.e. the added moment of inertia), and computations are facilitated. In 

 particular, solving the pair of coupled Equations [23] and [24] gives the 

 pitch amplitude 



[(T£/c) cos 3 + 2i E. (- w^ M + T/c] ] pgKAVexp (-Kh - iwt) 



e = . ^ ^ ,[26] 



(- w M + T/c) [T£ (1 + £/c) - Mg c^g - CO (I + I ') ] - (T£/c) 



As a second simplification we may assume that the cable length c 

 is very large compared to the arm length £. Then the equations of motion 

 are uncoupled, and 



2i 5pR Pg KAVexp (-Kh - icot) 



9 = ^ [27] 



T£ - Mg c^(. - ^ (I + I') 



We note that in this circumstance the pitch response is independent of the 

 heading angle 3. 



Finally we recall that the cable tension T is given by Equation 

 [2]. Thus 



2i C(.g Pg KA ¥ exp (- Kh - loot) 



pg ¥ £ - Mg (£ + ;„„) - i/ (I + I') 



XG' 



