中国物理B ›› 2003, Vol. 12 ›› Issue (4): 357-360.doi: 10.1088/1009-1963/12/4/302

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A set of the Lie symmetrical conservation laws for the rotational relativistic Birkhoffian system

蔡建乐1, 罗绍凯2   

  1. (1)Department of Physics, Hunan University, Changsha 410082, China; (2)Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China; Department of Physics, Hunan University, Changsha 410082, China
  • 收稿日期:2002-12-05 修回日期:2002-12-25 出版日期:2003-04-16 发布日期:2005-03-16
  • 基金资助:
    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).

A set of the Lie symmetrical conservation laws for the rotational relativistic Birkhoffian system

Luo Shao-Kai (罗绍凯)ab, Cai Jian-Le (蔡建乐)b    

  1. a Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China; b Department of Physics, Hunan University, Changsha 410082, China
  • Received:2002-12-05 Revised:2002-12-25 Online:2003-04-16 Published:2005-03-16
  • Supported by:
    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).

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摘要： 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.

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.

Key words: rotational relativistic, Birkhoffian system, Lie symmetry, non-noether conserved quantity

中图分类号:  (Special relativity)

  • 03.30.+p
02.20.Sv (Lie algebras of Lie groups)