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 πœ™ matrix 𝑀

(3.6) 2 𝑛 πœ™ ( 𝑉 1 , 𝑉 2 βˆ‘ ) = 𝑛 𝑖 = 1 𝛼 𝑖 | 𝑉 2 , 𝑖 | ( 𝐼 𝑛 0 0 β„³ βˆ’ 1 )
(3.12) 2 𝑛 πœ™ ( 𝑉 1 , 𝑉 2 βˆ‘ ) = 𝑛 𝑖 = 1 𝛼 𝑖 | 𝑉 2 , 𝑖 | ( 𝐼 𝑛 0 0 β„³ βˆ’ 1 )
(3.29)–(3.32) 𝑛 + 1 πœ™ ( 𝑑 , ( 𝐺 , π‘Ž , 𝑏 ) ) = πœ“ [ βˆ’ 𝛼 1 , 𝛼 1 ] Γ— β‹― Γ— [ βˆ’ 𝛼 𝑛 βˆ’ 1 , 𝛼 𝑛 βˆ’ 1 ] Γ— { 0 } Γ— { 0 } 𝛼 ( 𝐺 , π‘Ž , 𝑏 ) + 𝑛 π‘š | 𝑏 | (  𝐾 0 0 𝐼 2 )
(3.29)–(3.39) 𝑛 + 1 πœ™ ( 𝑑 , ( 𝐺 , π‘Ž , 𝑏 ) ) = πœ“ [ βˆ’ 𝛼 1 , 𝛼 1 ] Γ— β‹― Γ— [ βˆ’ 𝛼 𝑛 βˆ’ 1 , 𝛼 𝑛 βˆ’ 1 ] Γ— { 0 } Γ— { 0 } 𝛼 ( 𝐺 , π‘Ž , 𝑏 ) + 𝑛 π‘š | 𝑏 | (  𝐾 0 0 𝐼 2 )
(3.48) 𝑛 πœ™ ( 𝑋 ) = πœ“ [ βˆ’ 𝛼 1 , 𝛼 1 ] Γ— β‹― Γ— [ βˆ’ 𝛼 𝑛 , 𝛼 𝑛 ] ( 𝑋 ) 𝐾
(3.53) 𝑛 πœ™ ( 𝑋 ) = πœ“ [ βˆ’ 𝛼 1 , 𝛼 1 ] Γ— β‹― Γ— [ βˆ’ 𝛼 𝑛 , 𝛼 𝑛 ] ( 𝑋 ) 𝐾
(3.62) 𝑛 πœ™ ( 𝑋 ) = πœ“ [ βˆ’ 𝛼 1 , 𝛼 1 ] Γ— β‹― Γ— [ βˆ’ 𝛼 𝑛 , 𝛼 𝑛 ] ( 𝑋 )  𝐾

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