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## 留言板

Conformal invariance, Noether symmetry and Lie symmetry for holonomic mechanical system with variable mass

## Conformal invariance, Noether symmetry and Lie symmetry for holonomic mechanical system with variable mass

Chen Rong, Xu Xue-Jun
• #### Abstract

The conformal invariance of holonomic mechanical system with variable mass is studied. Firstly, the definition of conformal invariance for holonomic mechanical system with variable mass is given; secondly, the relation between the conformal invariance and the Noether symmetry is discussed, and the Noether conserved quantity led by the conformal invariance is obtained; finally, the relation between the conformal invariance and the Lie symmetry is discussed, and the Hojman conserved quantity caused by the conformal invariance of the systems is obtained. In the paper, an example is given to illustrate the application of the results.

#### References

 [1] Mei F X, Liu Y 1991 Advanced analytical mechanics (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔,刘瑞,罗勇 1991 高等分析力学(北京:北京理工大学出版社)] [2] 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)] [3] Galiullin A S, Gafarov G G, Malaishka R P 1997 Analytical Dynamics of Helmholtz Birkhoff and Nambu Systems (Moscow: UFN) (in Russian) [4] Li Y M, Zhang N 2010 Journal of Shangqiu Teachers College 26 55 (in Chinese) [李彦敏,张宁 2010 商丘师范学院学报 26 55] [5] Zhang Y 2009 Journal of Suzhou University of Science and Technology 26 1 (in Chinese) [张毅 2009 苏州科技学院学报 26 1] [6] Zhang Y, Xue Y 2009 Chinese Quarterly of Mechanics 30 216 (in Chinese) [张毅,薛纭 2009 力学季刊 30 216] [7] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 物理学报 58 22] [8] Robert M L, Matthew P 2001 J. Geom. Phys. 39 276 [9] 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 物理学报 58 5150] [10] Li YM2010 Journal of Yunnan University 32 52 (in Chinese ) [李彦敏 2010 云南大学学报 32 52]

#### Cited By

•  [1] Mei F X, Liu Y 1991 Advanced analytical mechanics (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔,刘瑞,罗勇 1991 高等分析力学(北京:北京理工大学出版社)] [2] 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)] [3] Galiullin A S, Gafarov G G, Malaishka R P 1997 Analytical Dynamics of Helmholtz Birkhoff and Nambu Systems (Moscow: UFN) (in Russian) [4] Li Y M, Zhang N 2010 Journal of Shangqiu Teachers College 26 55 (in Chinese) [李彦敏,张宁 2010 商丘师范学院学报 26 55] [5] Zhang Y 2009 Journal of Suzhou University of Science and Technology 26 1 (in Chinese) [张毅 2009 苏州科技学院学报 26 1] [6] Zhang Y, Xue Y 2009 Chinese Quarterly of Mechanics 30 216 (in Chinese) [张毅,薛纭 2009 力学季刊 30 216] [7] Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 物理学报 58 22] [8] Robert M L, Matthew P 2001 J. Geom. Phys. 39 276 [9] 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 物理学报 58 5150] [10] Li YM2010 Journal of Yunnan University 32 52 (in Chinese ) [李彦敏 2010 云南大学学报 32 52]
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•  Citation:
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##### Publishing process
• Received Date:  19 April 2011
• Accepted Date:  29 April 2011
• Published Online:  20 January 2012

## Conformal invariance, Noether symmetry and Lie symmetry for holonomic mechanical system with variable mass

• 1. Department of Physics, Zhejiang Normal University, Jinhua 321004, China

Abstract: The conformal invariance of holonomic mechanical system with variable mass is studied. Firstly, the definition of conformal invariance for holonomic mechanical system with variable mass is given; secondly, the relation between the conformal invariance and the Noether symmetry is discussed, and the Noether conserved quantity led by the conformal invariance is obtained; finally, the relation between the conformal invariance and the Lie symmetry is discussed, and the Hojman conserved quantity caused by the conformal invariance of the systems is obtained. In the paper, an example is given to illustrate the application of the results.

Reference (10)

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