9
Математическое моделирование механических систем
Ненулевые элементы матрицы следующие:
(
)
2
( )
1
,
1,6 ,
ii
ii
a
a i
ν
ν=
=
=
∑
( )
, ( 1, 2), ( ,
1,6);
ij
i j
a a
i j
ν ν
ν
=
ν =
=
i
ν
=
i
при
i
= 1, 2, 3;
i
ν
=
i
+ 3(ν – 1) при
i
= 4, 5, 6.
Обозначим
(
)
cos ,
sin
1,9 .
k
k
k
k
с
q s
q k
=
=
=
( )
(
)
(
)
(
)
11
22
33
1
2
2
2
( )
( )
2
4 4
5
6 5
( )
2
5 5
( )
6 6
( )
( )
( )
( )
14
1
1
21
31 6 5
( )
( )
( )
( )
15
2
2
21 6
31 6
,
2
,
,
,
,
,
,
,
x
y
y
x
a a a m 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
= = = +
=
+
+
= +
=
= κ κ = − α + α
= κ κ = α − α
(
)
(
)
(
)
( )
( )
( )
( )
24
3
3
22
32 6 5
( )
( )
( )
( )
25
4
4
22 6
32 6
( )
( )
( )
( )
34
5
5
23
33 6 5
( )
( )
( )
( )
35
6
6
23 6
33 6
( )
2 ( )
( )
4 5
7
7
6
,
,
,
,
,
,
,
,
,
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
s c
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
ν
ν ν
= κ κ = − α + α
= κ κ = α − α
= κ κ = − α + α
= κ κ = α − α
= + κ κ = −
(
)
6 6 5
( )
4 6
5
,
.
x
c c
a J c
ν
ν ν
ν ν
ν
ν
=
Здесь
( )
( )
( )
11
5 4
12
5
13
5 4
( )
( )
( )
21
6 5 4
6 4
22
6 5
23
6 5 4
6 4
( )
( )
( )
31
6 5 4
6 5
32
6 5
33
6 5 4
6 4
,
,
,
,
,
,
,
,
.
c c
s
c s
c s c s s
c c
c s s s c
s s c c s
s c
s s s c c
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
α =
α = α =
α = −
+
α =
α =
+
α =
+
α = −
α = −
+
Силовая функция СГП.
Силовая функция СГП
U
= –П, где П —
потенциальная энергия СГП, равная сумме потенциальных энергий
двух тел:
