
With centralized explicit Euler integration, the discrete-time states x
1,A
(n) and x
2,A
(n) are updated
at time t
nþ1
¼(n þ1)T in the sequence of steps as follows:
_
x
2
(n) ¼
€
x(n) ¼
1
M
[F(n) Kx
1, A
(n) Bx
2, A
(n)] (5:80)
_
x
1
(n) ¼ x
2, A
(n)(5:81)
x
2, A
(n þ 1) ¼ x
2, A
(n) þT
_
x
2
(n)(5:82)
) x
2, A
(n þ 1) ¼ x
2, A
(n) þ
T
M
[F(n) Kx
1, A
(n) Bx
2, A
(n)] (5:83)
x
1, A
(n þ 1) ¼ x
1, A
(n) þT
_
x
1
(n)(5:84)
) x
1, A
(n þ 1) ¼ x
1, A
(n) þ Tx
2, A
(n)(5:85)
Instead of starting with Equation 5.84 to update x
1,A
(n), the implicit Euler form can be used, that is,
the upd ated state x
1,A
(n þ1) is obtained from
x
1, A
(n þ 1) ¼ x
1, A
(n) þT
€
x
1
(n þ 1)(5:86)
) x
1, A
(n þ 1) ¼ x
1, A
(n) þ Tx
2, A
(n