中国物理B ›› 2001, Vol. 10 ›› Issue (5): 376-379.doi: 10.1088/1009-1963/10/5/302

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NOETHER'S THEOREM OF NONHOLONOMIC SYSTEMS OF NON-CHETAEV'S TYPE WITH UNILATERAL CONSTRAINTS

梅凤翔1, 李元成2, 张毅3, 梁景辉4   

  1. (1)Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China; (2)Department of Applied Physics, University of Petroleum, Dongying 257062, China; (3)Department of Basic Courses, Suzhou Institute of Urban Construction & Environmental Protection, Suzhou 215011, China; (4)Department of Physics, Shanxi Normal University, Linfen 041004, China
  • 收稿日期:2000-07-29 修回日期:2000-12-30 出版日期:2001-05-15 发布日期:2005-06-12
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No.19572018).

NOETHER'S THEOREM OF NONHOLONOMIC SYSTEMS OF NON-CHETAEV'S TYPE WITH UNILATERAL CONSTRAINTS

Li Yuan-cheng (李元成)a, Zhang Yi (张毅)b, Liang Jing-hui (梁景辉)c, Mei Feng-xiang(梅凤翔)d    

  1. a Department of Applied Physics, University of Petroleum, Dongying 257062, China; b Department of Basic Courses, Suzhou Institute of Urban Construction & Environmental Protection, Suzhou 215011, China; c Department of Physics, Shanxi Normal University, Linfen 041004, China; d Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China
  • Received:2000-07-29 Revised:2000-12-30 Online:2001-05-15 Published:2005-06-12
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No.19572018).

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摘要： In this paper, we present Noether's theorem and its inverse theorem for nonholonomic systems of non-Chetaev's type with unilateral constraints. We present first the principle of Jourdain for the system and, on the basis of the invariance of the differential variational principle under the infinitesimal transformations of groups, we have established Noether's theory for the above systems. An example is given to illustrate the application of the result.

关键词: analytical mechanics, unilateral constraint, nonholonomic system, Noether's theorem

Abstract: In this paper, we present Noether's theorem and its inverse theorem for nonholonomic systems of non-Chetaev's type with unilateral constraints. We present first the principle of Jourdain for the system and, on the basis of the invariance of the differential variational principle under the infinitesimal transformations of groups, we have established Noether's theory for the above systems. An example is given to illustrate the application of the result.

Key words: analytical mechanics, unilateral constraint, nonholonomic system, Noether's theorem

中图分类号:  (Calculus of variations)

  • 02.30.Xx
02.20.-a (Group theory)