111


 a4 S4 + d3 pz (9.42)


 a4 S5 + S45 (a2 C3 + al C23) = t p (9.43)


a4 C4 (a2 C3 + al C23) + dg a4 S4 + al a2 C2 =

 [p.p al2 -a2 a42 -d32]/2. (9.44)


Expression for ltx, it y, px', and 1py provide the additional equations,


 C23 S45 = 1tx (9.45)

 S23 S45 = It (9.46)

 a4 C4 C23 + a2 C2 + al px (9.47)

 a4 C4 S23 + a2 S2 = 1py (9.48)


If the function f is defined from equation (9.43), then for a given value of el, the corresponding values of S5, S45, C3 and C23 must be computed before


f(e1) = a4 S5 + S45 (a2 C3 + a1 C23) t.p (9.49)


can be evaluated.

Computing f

 Given 91, the components of It and 1p are computed from Eqs (9.39) and (9.40). The value of C45 and S45 are then given by Eq. (9.41)


 C45 = itx)

and


S45 = u45 Trig(C45)

..