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Chin. Phys., 2003, Vol. 12(4): 357-360    DOI: 10.1088/1009-1963/12/4/002
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A set of the Lie symmetrical conservation laws for the rotational relativistic Birkhoffian system

Cai Jian-Lea, Luo Shao-Kaib
a Department of Physics, Hunan University, Changsha 410082, China; b Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China; Department of Physics, Hunan University, Changsha 410082, China
Abstract  For a rotational relativistic Birkhoffian system, a set of the Lie symmetries and conservation laws is given under infinitesimal transformations. On the basis of the invariance of rotational relativistic Birkhoffian equations under infinitesimal transformations, Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The determining equations of Lie symmetries are given, and a new type of non-noether conserved quantities are directly obtained from Lie symmetries of the system. An example is given to illustrate the application of the results.
Keywords:  Birkhoffian system      Lie symmetry      non-noether conserved quantity      rotational relativistic  
Received:  05 December 2002      Revised:  25 December 2002      Published:  16 March 2005
PACS:  03.30.+p (Special relativity)  
  02.20.Sv (Lie algebras of Lie groups)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 19972010), the Natural Science Foundation of Henan Province, China (Grant Nos 998040080 and 984053100), and the Scientific Research Foundation of the Education Bureau of Hunan Province, China (Grant No 02C033).

Cite this article: 

Cai Jian-Le, Luo Shao-Kai A set of the Lie symmetrical conservation laws for the rotational relativistic Birkhoffian system 2003 Chin. Phys. 12 357

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