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The conformal invariance of a system with unilateral Chetaev non-holonomic is studied, and its definition is given. The relation between the conformal invariance and the Noether symmetry is discussed. Finally, the relation between the conformal invariance and the Lie symmetry is discussed, and the Hojman conserved quantity due to the conformal invariance of the systems is obtained. In the paper, an example is given to illustrate the application of the results.
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Keywords:
- unilateral Chetaev non-holonomic constraints /
- conformal invariance /
- conformal factor /
- conserved quantity
[1] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 2004 约束力学系统的对称性与守恒量(北京:北京理工大学出版社)]
[2] Galiullin A S, Gafarov G G, Malaishka R P 1997 Analytical Dynamics of Helmholtz Birkhoff and Nambu Systems (Moscow: UFN) (in Russian)
[3] Cai J L, Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese) [蔡建乐, 梅凤翔 2008 57 5369]
[4] Zhang Y, Xue Y 2009 Chinese Quarterly of Mechanics 30 216 (in Chinese) [张毅, 薛纭 2009 力学季刊 30 216]
[5] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[6] Chen X W, Zhao Y H, Liu C 2009 Acta Phys. Sin. 58 5150 (in Chinese) [陈向炜, 赵永红, 刘畅 2009 58 5150]
[7] Liu C, Liu S X, Mei F X, Guo Y X 2009 Chin. Phys. B 18 0856
[8] Zhang M J, Fang J H, Lu K, Zhang K J, Li Y 2009 Chin. Phys. B 18 4650
[9] Liu C, Mei F X, Guo Y X 2009 Chin. Phys. B 18 395
[10] Xia L L, Cai J L 2010 Chin. Phys. B 19 040302
[11] Luo Y P, Fu J L 2010 Chin. Phys. B 19 090303
[12] Zhang Y 2004 Acta Phys. Sin. 53 331 (in Chinese) [张毅 2004 53 331]
[13] Zhang Y 2006 Acta Phys. Sin. 55 504 (in Chinese) [张毅 2006 55 504]
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[1] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 2004 约束力学系统的对称性与守恒量(北京:北京理工大学出版社)]
[2] Galiullin A S, Gafarov G G, Malaishka R P 1997 Analytical Dynamics of Helmholtz Birkhoff and Nambu Systems (Moscow: UFN) (in Russian)
[3] Cai J L, Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese) [蔡建乐, 梅凤翔 2008 57 5369]
[4] Zhang Y, Xue Y 2009 Chinese Quarterly of Mechanics 30 216 (in Chinese) [张毅, 薛纭 2009 力学季刊 30 216]
[5] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[6] Chen X W, Zhao Y H, Liu C 2009 Acta Phys. Sin. 58 5150 (in Chinese) [陈向炜, 赵永红, 刘畅 2009 58 5150]
[7] Liu C, Liu S X, Mei F X, Guo Y X 2009 Chin. Phys. B 18 0856
[8] Zhang M J, Fang J H, Lu K, Zhang K J, Li Y 2009 Chin. Phys. B 18 4650
[9] Liu C, Mei F X, Guo Y X 2009 Chin. Phys. B 18 395
[10] Xia L L, Cai J L 2010 Chin. Phys. B 19 040302
[11] Luo Y P, Fu J L 2010 Chin. Phys. B 19 090303
[12] Zhang Y 2004 Acta Phys. Sin. 53 331 (in Chinese) [张毅 2004 53 331]
[13] Zhang Y 2006 Acta Phys. Sin. 55 504 (in Chinese) [张毅 2006 55 504]
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