Substituting the values of R(0) and R(r) in Eqs. 5.48 and 5.49 gives 
co 
o2 1+2 S a’ cosrw 
r=1 
GE i ; 
or 1+2 SS Re {are | 
r=1 
o- 9 . P 
= = F + 2'Ke {aei# + (ae)? + (ae)? +- - 1] 
2 +m 
EEF 1.9) Cad 
—aet 
1 +iasi 
se cele Se acos@ ase 
270 (1-—a cos w)-—i asin w 
Ge 14 2 A L08 WU =a cos) ~ a* sin’ w _& ar 
On (1—acosw)*+a*sinw 29 1—2acosw+a-’ 
here Re {-} indicates to take the real part of a function {-}. 
; az 
Inserting Eq. 5.37, that is 02 = = gives 
oz 1 
SO) = es 
22 (1—2acosw +a*) 
2 2 
O, 0. 
= £ = = (5.50) 
on | 1-ae|2 a | ave)? 
Therefore, 
2 2 2 
Ox 1- Ox 1+ 
5(0) = 2 a : _Oxita 
2x (1-a) 2x 1-a 
2 
Get 3 (5.51) 
27 (1 —a) 
111 
