8
Ю.В. Журавлёв
(
)
( ) 2
( ) 2
( ) 2
( ) 2
( ) 2
( ) 2
11 0
22 0
33 0
44
55
66
( )
( )
( )
( )
14 0
15 0
24 0
25 0
( )
( )
( )
( )
34 0
35 0
45
46
1
2
2
2
2
2
2
2
2
2
,
T a x a y a z a
a
a
a x
a x
a y
a y
a z
a z
a
a
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν
ν ν
ν ν
=
+ + + ψ + ϑ + ϕ +
+ ψ +
ϑ +
ψ +
ϑ +
+
ψ +
ϑ + ψ ϑ + ψ ϕ
где
( )
(
)
(
)
(
)
( )
( )
( )
11
22
33
2
2
( )
( )
( )
2
44
( )
( )
2
55
( )
( )
66
( )
( )
( )
( )
( )
14
1
1
21
31
( )
( )
( )
( )
( )
15
2
2
21
31
,
2
,
,
,
,
,
,
,
x
y
y
x
a a a m
a J c
J m b c c
a J m b
a J
a m b
c c
a m b
c
s
ν
ν
ν
ν
ν
ν
ν
ν
ν ν
ν ν
ν
ν
ν ν
ν
ν
ν
ν
ν
ν
ν
ν ν
ν ν
ν
ν
ν
ν
ν
ν ν
ν
ν
= = =
= ϑ +
+
ϕ ϑ
= +
=
= κ κ = − α + α ϕ ϑ
= κ κ = α ϕ − α ϕ
(
)
(
)
(
)
( )
( )
( )
( )
( )
24
3
3
22
32
( )
( )
( )
( )
( )
25
4
4
22
32
( )
( )
( )
( )
( )
34
5
5
23
33
( )
( )
( )
( )
( )
35
6
6
23
33
( )
( )
2 ( )
45
7
7
,
,
,
,
,
,
,
,
,
y
a m b
c c
a m b
c
s
a m b
c c
a m b
c
s
a J m b
ν
ν
ν
ν
ν
ν ν
ν ν
ν
ν
ν
ν
ν
ν ν
ν
ν
ν
ν
ν
ν
ν
ν ν
ν ν
ν
ν
ν
ν
ν
ν ν
ν
ν
ν
ν
ν
ν ν
= κ κ = − α + α ϕ ϑ
= κ κ = α ϕ − α ϕ
= κ κ = − α + α ϕ ϑ
= κ κ = α ϕ − α ϕ
= + κ κ
(
)
( )
( )
( )
46
,
.
x
s c c c
a J c
ν
ν
ν
ν ν
ν
ν
ν
= ϕ − ϕ ϕ ϑ
= ϑ
Полная кинетическая энергия СГП, равная
2
1
,
T T
ν
ν=
=
∑
примет вид
квадратичной формы
1 .
2
T q Aq
′
=
Матрица
А
— симметрическая и
сильно разреженная:
11
14
15
17
18
22
24
25
27
28
33
34
35
37
38
44
45
46
55
66
77
78
79
88
99
0 0
0
0
0
0
0
0
0
0 0 0
*
0 0 0 0 .
*
0 0 0
*
0
a
a a
a a
a
a a
a a
a a a
a a
a a a
A
a
a
a a a
a
a
⎛
⎞
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
∗
⎜
⎟
⎜
⎟
=
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
⎝
⎠
