中国物理B ›› 2000, Vol. 9 ›› Issue (6): 401-407.doi: 10.1088/1009-1963/9/6/001

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SYMMETRIES AND CONSERVED QUANTITIES FOR SYSTEMS OF GENERALIZED CLASSICAL MECHANICS

尚玫1, 梅凤翔1, 张毅2   

  1. (1)Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China; (2)Department of Basic Courses, Suzhou Institute of Urban Construction & Environmental Protection, Suzhou 215011, China
  • 收稿日期:1999-09-23 修回日期:1999-12-20 出版日期:2000-06-15 发布日期:2005-06-12
  • 基金资助:
    Project supported by the Doctoral Program Foundation of Institution of Higher Education of China.

SYMMETRIES AND CONSERVED QUANTITIES FOR SYSTEMS OF GENERALIZED CLASSICAL MECHANICS

Zhang Yi (张毅)a, Shang Mei (尚玫)b, Mei Feng-xiang (梅凤翔)b   

  1. a Department of Basic Courses, Suzhou Institute of Urban Construction & Environmental Protection, Suzhou 215011, China; b Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China
  • Received:1999-09-23 Revised:1999-12-20 Online:2000-06-15 Published:2005-06-12
  • Supported by:
    Project supported by the Doctoral Program Foundation of Institution of Higher Education of China.

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摘要： In this paper, the symmetries and the conserved quantities for systems of generalized classical mechanics are studied. First, the generalized Noether's theorem and the generalized Noether's inverse theorem of the systems are given, which are based upon the invariant properties of the canonical action with respect to the action of the infinitesimal transformation of r-parameter finite group of transformation; second, the Lie symmetries and conserved quantities of the systems are studied in accordance with the Lie's theory of the invariance of differential equations under the transformation of infinitesimal groups; and finally, the inner connection between the two kinds of symmetries of systems is discussed.

Abstract: In this paper, the symmetries and the conserved quantities for systems of generalized classical mechanics are studied. First, the generalized Noether's theorem and the generalized Noether's inverse theorem of the systems are given, which are based upon the invariant properties of the canonical action with respect to the action of the infinitesimal transformation of r-parameter finite group of transformation; second, the Lie symmetries and conserved quantities of the systems are studied in accordance with the Lie's theory of the invariance of differential equations under the transformation of infinitesimal groups; and finally, the inner connection between the two kinds of symmetries of systems is discussed.

中图分类号:  (Classical electromagnetism, Maxwell equations)

  • 03.50.De
45.05.+x (General theory of classical mechanics of discrete systems)