-MogZQ+P ^Ji ^ ^B. + g ^ J^ m(z/)xdz.' [ 1 5e] 



i=0 i=l 



N N 



[15f] 



i = i==l 



mlz.') is the mass per unit length of the spar itself. The integral is taken 

 over the length L of the spar. This length generally extends from z-' = - H 

 to some value of z-' greater than zero, x and y are the distances from the 

 fixed reference fram^e to a point on the axis of the i spar. 

 The moment of inertia I^ about the x-axis is 



li = \ m(zi')(y2 + z2)dzi' 



where y = ag sin 6^ + yg + V a-Q ^°^ Q:^- az( + . . . , and 

 z = z^' + zq + a aQ sin 9^ - (3 aQ cos 9^ + . . . , 



the omitted terms being of higher order in the small motion variables. 

 Since I- is multiplied by a, we need keep only the zero-order terms in 

 1^ . Clearly then. 



li = \ m(z.') [a^ sin^Bi + z-'^] dz-' 



'L 



to the required order in small quantities; that is, I^ has the same value as 

 in the equilibrium position. Similarly, 



Ji = I m(zi')(x2 + z2)dzi' 



= f m(z.-')[ao cos^9i+ z.'^ldz.' 



«' T 



16 



