12/25/2008
1
Nguyn Quang Minh
(
)
( )
( )
=
=
=




nr
n
n
LLL
LLL
LLL
ϕ
ϕ
ϕ
12/25/2008
2




=
=+++++
=++
o
o
Phương trình ñiu kin
Mi trño tha scho mt
phương trình ñiu kin, r trño
tha >r phương trình ñiu kin
12/25/2008
3
Dùng khai trin Taylor, giñn shng bc
nht:
Áp dng cho các phương trình ñiu kin,
chúng ta scó:
( )
(
)

=+
∂
∂
+
∂
∂
+= v
L
v
L
LLLLLL
ño
n
ñoño
n
ϕ
ϕ
ϕϕ
( )
(
)

=+
∂
∂
+
∂
∂
+= v
L
v
L
LLLLLL
ii
ño
n
ñoño
ini
ϕ
ϕϕ
(
)
( )
( )
r
ño
n
ñoño
rn
n
rrr
b
ño
n
ñoño
n
n
a
ño
n
ñoño
n
n
LLLr
L
r
L
r
L
LLLb
L
b
L
b
L
LLLa
L
a
L
a
L
ωϕ
ϕϕϕ
ωϕ
ϕϕϕ
ωϕ
ϕ
ϕ
ϕ
==
∂
∂
=
∂
∂
=
∂
∂
==
∂
∂
=
∂
∂
=
∂
∂
==
∂
∂
=
∂
∂
=
∂
∂




12/25/2008
4




=++++
=++++
=
+
+
+
+
rnn
bnn
ann
vrvrvr
vbvbvb
vavava
ω
ω
ω





=
+
=
+
W
BV
v
v
v
rrr
bbb
aaa
rn
n
n
ω
ω
ω
12/25/2008
5
[ ]
[ ]
[ ]

=
+
⇒
=+
=+
=+
⇒
=
+






r
b
a
r
n
n
n
rv
bv
av
v
v
v
rrr
bbb
aaa
ω
ω
ω
ω
ω
ω
[
]
[ ]
( )
[ ]
( )
[ ]
( )
( )









−
×
−
−
−
==+
=+=+⇒
=
=
=⇒−==
∂
Φ∂
+−=
+−−+−+−=
==Φ
rr
TT
rrbbaa
T
T
v
rvKbvKavK
pvv
ωωω
=
r
b
a
K
K
K
