A2v (X2) = .5(Ai (Xi) + A2 (X2))
(X1) +( (X, )2 +. 04A2 (X2))5
t2 (X(X2)
V2 (X2) = V1 (Xi) + A2V (X2) t2 (X2)
At position Xn = X (n-1) +.01
A (Xn) 2K((Lmax -L,) +dmn) cosxn -(.5C+j)Ff -2W, cose0-0,) cos, (2.17)
M (.C+ j)
Anv (Xn)= .5(An-1 (Xn-1) + An (Xn))
tn (Xn) -V- (X,_1 ) + ( n_1 (X, 1 )2 +.04A, (X,)) 5
2A,, (X,,)
Vn (Xn) = Vn-1 (Xn-1) + AnV (Xn) tn (Xn)
Total time taken to deploy the layer,
(2.18)
(2.19)
(2.20)
(2.21)
TT =
1=1
Total time taken to deploy the structure
N
TTS = 2 ZTT
j=1
(2.22)
Hence the instantaneous time, velocity and acceleration with respect to position for
any layer is determined. The total time taken to deploy the structure is also determined.
The Matlab program "PROG2T" as shown in the appendix A, is used to perform these
calculations.
2.4.3 Alteration of the Stiffness of the Springs
From equation (2.21) the time taken to deploy the various layers on any side is
determined. For reasons due to uniformity and better performance (more importantly in
space applications) the stiffness of the springs should be designed in such a way that the