J ≡ I1 - I2 + I3 - I 4 - I5 + I 6
{ }[ ]{η }+ 1 {}[ ]{}
1
1
{η}[ 1 ] η} ηB
$ K {$ -
T
T
T
B
(62)
K
K $
=
$
2
3
2
2
2
- {η }[ ] } {Q }{η } {Q }{}
K { -
Γ T
T
T
Γ
$ +
$
4
5
6
Since J is stationary, the following must be true for the solution of the problem :
J
=0
i = 1, 2, 3, ...., N
(63)
η
$i
and
J
=0
j = 1, 2, 3, ..., M
(64)
j
These relations give
[ 1 ] η} [ 2 ] ηB} [ 4 ] }= {Q 5}
K {$ - K {$ - K {
(65)
and
{}
[
K 3 ] } [ 4 ] ηΓ = - {Q 6 }
{ -K T $
(66)
From Equation 66, we have
{m} - [ 3 ]- 1{Q 6 } [ 3 ]- 1[ 4 ]T {ηΓ}
$
=K
+K
K
(67)
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