中国物理B ›› 2008, Vol. 17 ›› Issue (12): 4365-4368.doi: 10.1088/1674-1056/17/12/005

• GENERAL • 上一篇    下一篇

Routh method of reduction for Birkhoffian systems in the event space

张毅   

  1. College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China
  • 收稿日期:2008-03-23 修回日期:2008-04-18 出版日期:2008-12-20 发布日期:2008-12-20
  • 基金资助:
    Project supported by the Natural Science Foundation of Higher Education Institution of Jiangsu Province, China (Grant Nos 04KJA130135 and 08KJB130002).

Routh method of reduction for Birkhoffian systems in the event space

Zhang Yi (张毅)   

  1. College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China
  • Received:2008-03-23 Revised:2008-04-18 Online:2008-12-20 Published:2008-12-20
  • Supported by:
    Project supported by the Natural Science Foundation of Higher Education Institution of Jiangsu Province, China (Grant Nos 04KJA130135 and 08KJB130002).

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摘要： For a Birkhoffian system in the event space, this paper presents the Routh method of reduction. The parametric equations of the Birkhoffian system in the event space are established, and the definition of cyclic coordinates for the system is given and the corresponding cyclic integral is obtained. Through the cyclic integral, the order of the system can be reduced. The Routh functions for the Birkhoffian system in the event space are constructed, and the Routh method of reduction is successfully generalized to the Birkhoffian system in the event space. The results show that if the system has a cyclic integral, then the parametric equations of the system can be reduced at least by two degrees and the form of the equations holds. An example is given to illustrate the application of the results.

Abstract: For a Birkhoffian system in the event space, this paper presents the Routh method of reduction. The parametric equations of the Birkhoffian system in the event space are established, and the definition of cyclic coordinates for the system is given and the corresponding cyclic integral is obtained. Through the cyclic integral, the order of the system can be reduced. The Routh functions for the Birkhoffian system in the event space are constructed, and the Routh method of reduction is successfully generalized to the Birkhoffian system in the event space. The results show that if the system has a cyclic integral, then the parametric equations of the system can be reduced at least by two degrees and the form of the equations holds. An example is given to illustrate the application of the results.

Key words: event space, Birkhoffian system, reduction, cyclic integral

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

  • 45.05.+x
02.30.Jr (Partial differential equations)