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Mathematical Problems in Engineering
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Table of Contents
Special Issues
Mathematical Problems in Engineering
/
2009
/
Article
/
Tab 1
/
Research Article
Theoretical Study of a Chain Sliding on a Fixed Support
Table 1
The dimension of the system, the convex function and the symmetric positive definite matrix used for the above described mechanical models.
System
𝑝
function
𝜙
matrix
𝑀
(
3.6
)
2
𝑛
𝜙
(
𝑉
1
,
𝑉
2
∑
)
=
𝑛
𝑖
=
1
𝛼
𝑖
|
𝑉
2
,
𝑖
|
(
𝐼
𝑛
0
0
ℳ
−
1
)
(
3.12
)
2
𝑛
𝜙
(
𝑉
1
,
𝑉
2
∑
)
=
𝑛
𝑖
=
1
𝛼
𝑖
|
𝑉
2
,
𝑖
|
(
𝐼
𝑛
0
0
ℳ
−
1
)
(
3.29
)–(
3.32
)
𝑛
+
1
𝜙
(
𝑡
,
(
𝐺
,
𝑎
,
𝑏
)
)
=
𝜓
[
−
𝛼
1
,
𝛼
1
]
×
⋯
×
[
−
𝛼
𝑛
−
1
,
𝛼
𝑛
−
1
]
×
{
0
}
×
{
0
}
𝛼
(
𝐺
,
𝑎
,
𝑏
)
+
𝑛
𝑚
|
𝑏
|
(
𝐾
0
0
𝐼
2
)
(
3.29
)–(
3.39
)
𝑛
+
1
𝜙
(
𝑡
,
(
𝐺
,
𝑎
,
𝑏
)
)
=
𝜓
[
−
𝛼
1
,
𝛼
1
]
×
⋯
×
[
−
𝛼
𝑛
−
1
,
𝛼
𝑛
−
1
]
×
{
0
}
×
{
0
}
𝛼
(
𝐺
,
𝑎
,
𝑏
)
+
𝑛
𝑚
|
𝑏
|
(
𝐾
0
0
𝐼
2
)
(
3.48
)
𝑛
𝜙
(
𝑋
)
=
𝜓
[
−
𝛼
1
,
𝛼
1
]
×
⋯
×
[
−
𝛼
𝑛
,
𝛼
𝑛
]
(
𝑋
)
𝐾
(
3.53
)
𝑛
𝜙
(
𝑋
)
=
𝜓
[
−
𝛼
1
,
𝛼
1
]
×
⋯
×
[
−
𝛼
𝑛
,
𝛼
𝑛
]
(
𝑋
)
𝐾
(
3.62
)
𝑛
𝜙
(
𝑋
)
=
𝜓
[
−
𝛼
1
,
𝛼
1
]
×
⋯
×
[
−
𝛼
𝑛
,
𝛼
𝑛
]
(
𝑋
)
𝐾