For shaft segment (1) as shown in Figure 8.35(b), the state vector can be related as

(a)

For second branch, the state vector can be written as

(b)

End conditions for the overhang rotor as shown in Figure 8.35(a) can be written as

(c)   (d)     (e)

From the first shaft segment, i.e., equation (a), on application of end conditions of equation (c), we have

(f)

(g)     (h)

From equation (f), the first set of equation gives

(i)

On using equation (i) into equation (f), we get state vectors in the left of station 1 as

(j)

Now noting equations (d) and (j) we can have state vectors in the right of station 1 as

(k)

Equation (k) can be written as

(l)

Equation (l) can be written in a standard form as

(m)