Generalized energy integral and reduction of rotational relativistic Birkhoffian system

doi:10.1088/1009-1963/11/11/301

中国物理B ›› 2002, Vol. 11 ›› Issue (11): 1097-1100.doi: 10.1088/1009-1963/11/11/301

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Generalized energy integral and reduction of rotational relativistic Birkhoffian system

罗绍凯

Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China

收稿日期:2002-04-18 修回日期:2002-06-03 出版日期:2002-11-12 发布日期:2005-06-12
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No 19972010), the Natural Science Foundation of Hunan Province, China (Grant Nos 998040080, 984053100, 934060800).

Generalized energy integral and reduction of rotational relativistic Birkhoffian system

Luo Shao-Kai (罗绍凯)

Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China

Received:2002-04-18 Revised:2002-06-03 Online:2002-11-12 Published:2005-06-12
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 19972010), the Natural Science Foundation of Hunan Province, China (Grant Nos 998040080, 984053100, 934060800).

摘要/Abstract

摘要： We study the order reduction method of the rotational relativistic Birkhoffian equations. For a rotational relativistic autonomous Birkhoffian system, if the conservative law of the Birkhoffian holds, the conservative quantity can be called the generalized energy integral. Through the generalized energy integral, the order of the system can be reduced. If the rotational relativistic Birkhoffian system has a generalized energy integral, then the Birkhoffian equations can be reduced by at least two degrees and the Birkhoffian form can be kept. An example is given to illustrate the application of the result.

Abstract: We study the order reduction method of the rotational relativistic Birkhoffian equations. For a rotational relativistic autonomous Birkhoffian system, if the conservative law of the Birkhoffian holds, the conservative quantity can be called the generalized energy integral. Through the generalized energy integral, the order of the system can be reduced. If the rotational relativistic Birkhoffian system has a generalized energy integral, then the Birkhoffian equations can be reduced by at least two degrees and the Birkhoffian form can be kept. An example is given to illustrate the application of the result.

Key words: rotational relativity, Birkhoffian equation, order reduction method, generalized energy integral

中图分类号: (General theory of classical mechanics of discrete systems)

45.05.+x

02.30.Rz (Integral equations)

罗绍凯. Generalized energy integral and reduction of rotational relativistic Birkhoffian system[J]. 中国物理B, 2002, 11(11): 1097-1100.

Luo Shao-Kai (罗绍凯). Generalized energy integral and reduction of rotational relativistic Birkhoffian system[J]. Chinese Physics, 2002, 11(11): 1097-1100.

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Generalized energy integral and reduction of rotational relativistic Birkhoffian system

Generalized energy integral and reduction of rotational relativistic Birkhoffian system

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