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Chin. Phys. B, 2009, Vol. 18(11): 4636-4642    DOI: 10.1088/1674-1056/18/11/005
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Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space

Zhang Yi(张毅)
College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China
Abstract  This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.
Keywords:  holonomic system      conformal invariance      symmetry      event space  
Received:  13 August 2008      Revised:  09 September 2008      Accepted manuscript online: 
PACS:  45.05.+x (General theory of classical mechanics of discrete systems)  
  02.20.Qs (General properties, structure, and representation of Lie groups)  
  02.40.-k (Geometry, differential geometry, and topology)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No10772025) and the Natural Science Foundation of Higher Education Institution of Jiangsu Province of China (Grant No 08KJB130002).

Cite this article: 

Zhang Yi(张毅) Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space 2009 Chin. Phys. B 18 4636

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