中国物理B ›› 2002, Vol. 11 ›› Issue (6): 523-528.doi: 10.1088/1009-1963/11/6/301

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Algebraic structure and Poisson integrals of a rotational relativistic Birkhoff system

郭永新1, 罗绍凯2, 陈向炜3   

  1. (1)Department of Physics, Liaoning University, Shenyang 110036, China; (2)Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China; Institute of Mathematical Mechanics and Mathematical Physics, Shangqiu Teachers College, Shangqiu 476000, China; (3)Institute of Mathematical Mechanics and Mathematical Physics, Shangqiu Teachers College, Shangqiu 476000, China
  • 收稿日期:2001-11-01 修回日期:2001-12-26 出版日期:2002-06-12 发布日期:2005-06-12
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 19972010), and by the Natural Science Foundation of Henan Province, China (Grant Nos 998040080, 984053100 and 934060800) and by the Natural Science Foundation of Liaoning Province, China (Grant Nos 990111004 and 20021004).

Algebraic structure and Poisson integrals of a rotational relativistic Birkhoff system

 Luo Shao-Kaiab, Chen Xiang-Wei (陈向炜)b, Guo Yong-Xin (郭永新)c   

  1. a Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China; b ; Institute of Mathematical Mechanics and Mathematical Physics, Shangqiu Teachers College, Shangqiu 476000, China; c Department of Physics, Liaoning University, Shenyang 110036, China
  • Received:2001-11-01 Revised:2001-12-26 Online:2002-06-12 Published:2005-06-12
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 19972010), and by the Natural Science Foundation of Henan Province, China (Grant Nos 998040080, 984053100 and 934060800) and by the Natural Science Foundation of Liaoning Province, China (Grant Nos 990111004 and 20021004).

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摘要： We have studied the algebraic structure of the dynamical equations of a rotational relativistic Birkhoff system. It is proven that autonomous and semi-autonomous rotational relativistic Birkhoff equations possess consistent algebraic structure and Lie algebraic structure. In general, non-autonomous rotational relativistic Birkhoff equations possess no algebraic structure, but a type of special non-autonomous rotational relativistic Birkhoff equation possesses consistent algebraic structure and consistent Lie algebraic structure. Then, we obtain the Poisson integrals of the dynamical equations of the rotational relativistic Birkhoff system. Finally, we give an example to illustrate the application of the results.

Abstract: We have studied the algebraic structure of the dynamical equations of a rotational relativistic Birkhoff system. It is proven that autonomous and semi-autonomous rotational relativistic Birkhoff equations possess consistent algebraic structure and Lie algebraic structure. In general, non-autonomous rotational relativistic Birkhoff equations possess no algebraic structure, but a type of special non-autonomous rotational relativistic Birkhoff equation possesses consistent algebraic structure and consistent Lie algebraic structure. Then, we obtain the Poisson integrals of the dynamical equations of the rotational relativistic Birkhoff system. Finally, we give an example to illustrate the application of the results.

Key words: rotational relativity, Birkhoff equation, algebraic structure, Poisson integral

中图分类号:  (Lie algebras of Lie groups)

  • 02.20.Sv
02.30.Jr (Partial differential equations) 02.30.Rz (Integral equations)