
Setting Q
3
(s) ¼0 in Equation 4.197 and solving Equations 4.195 through 4.198 for X
3
(s) and X
4
(s),
X
3
(s) ¼
s þ k
1
k
21
0 k
41
k
12
s þ k
2
00
0 k
23
00
k
14
0 Q
4
(s) s þ k
4
s þ k
1
k
21
0 k
41
k
12
s þ k
2
00
0 k
23
s þ k
3
0
k
14
0 k
34
s þ k
4
(4:201)
X
4
(s) ¼
s þ k
1
k
21
00
k
12
s þ k
2
00
0 k
23
s þ k
3
0
k
14
0 k
34
Q
4
(s)
s þ k
1
k
21
0 k
41
k
12
s þ k
2
00
0 k
23
s þ k
3
0
k
14
0 k
34
s þ k
4
(4:202)
Evaluation of the determinants in Equations 4.201 and 4.202 is a tedious process left as an exercise
problem. The results are as follows:
X
3
(s) ¼
a
0
s
4
þ a
3
s
3
þ a
2
s
2
þ a
1
s þ a
0
Q
4
(s)(4:203)
X
4
(s) ¼
s
3
þ b
2
s
2
þ b
1
s þ b
0
s
4
þ a
3
s
3
þ a
2
s
2