Mathematical Problems in Engineering

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