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.
Received: 23 March 2008
Revised: 18 April 2008
Accepted manuscript online:
PACS:
45.05.+x
(General theory of classical mechanics of discrete systems)
Fund: Project supported by the Natural
Science Foundation of Higher Education Institution of Jiangsu
Province, China (Grant Nos 04KJA130135 and 08KJB130002).
Cite this article:
Zhang Yi (张毅) Routh method of reduction for Birkhoffian systems in the event space 2008 Chin. Phys. B 17 4365
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