中国物理B ›› 2009, Vol. 18 ›› Issue (8): 3145-3149.doi: 10.1088/1674-1056/18/8/008

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Symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates

吴惠彬, 梅凤翔   

  1. School of Science, Beijing Institute of Technology, Beijing 100081, China
  • 收稿日期:2008-10-18 修回日期:2008-12-12 出版日期:2009-08-20 发布日期:2009-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025) and the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022), and the Fund for Fundamental Research of Beijing Institute of Technology (Grant No 20070742005).

Symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates

Wu Hui-Bin(吴惠彬)† and Mei Feng-Xiang(梅凤翔)   

  1. School of Science, Beijing Institute of Technology, Beijing 100081, China
  • Received:2008-10-18 Revised:2008-12-12 Online:2009-08-20 Published:2009-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025) and the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022), and the Fund for Fundamental Research of Beijing Institute of Technology (Grant No 20070742005).

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摘要： This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exists a conserved quantity and the form of the conserved quantity are obtained. Finally, an example is shown to illustrate the application of the results.

Abstract: This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exists a conserved quantity and the form of the conserved quantity are obtained. Finally, an example is shown to illustrate the application of the results.

Key words: quasi-coordinate, holonomic system, symmetry of Lagrangians, conserved quantity

中图分类号:  (Lagrangian and Hamiltonian mechanics)

  • 45.20.Jj
02.20.Sv (Lie algebras of Lie groups)