中国物理B ›› 2004, Vol. 13 ›› Issue (11): 1784-1789.doi: 10.1088/1009-1963/13/11/002

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Non-Noether symmetries and conserved quantities of the Lagrange mechano-electrical systems

傅景礼1, 陈立群2, 刘荣万3   

  1. (1)Department of Applied Physics, Zhejiang University of Science, Hangzhou 310018, China; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; (2)Department of Mechanics, Shanghai University, Shanghai 200072, China; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; (3)Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; Shaoguan University, Shaogua
  • 收稿日期:2004-02-25 修回日期:2004-05-08 出版日期:2004-11-20 发布日期:2005-06-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10372053) and the Natural Science Foundation of Henan Province (Grant No 0311011400).

Non-Noether symmetries and conserved quantities of the Lagrange mechano-electrical systems

Fu Jing-Li (傅景礼)ac, Chen Li-Qun (陈立群)bc, Liu Rong-Wan (刘荣万)cd   

  1. a Department of Applied Physics, Zhejiang University of Science, Hangzhou 310018, Chinab Department of Mechanics, Shanghai University, Shanghai 200072, China; c Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, Chinad Shaoguan University, Shaoguan 512005, China
  • Received:2004-02-25 Revised:2004-05-08 Online:2004-11-20 Published:2005-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10372053) and the Natural Science Foundation of Henan Province (Grant No 0311011400).

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摘要： This paper focuses on studying non-Noether symmetries and conserved quantities of Lagrange mechano-electrical dynamical systems. Based on the relationships between the motion and Lagrangian, we present conservation laws on non-Noether symmetries for Lagrange mechano-electrical dynamical systems. A criterion is obtained on which non-Noether symmetry leads to Noether symmetry of the systems. The work also gives connections between the non-Noether symmetries and Lie point symmetries, and further obtains Lie invariants to form a complete set of non-Noether conserved quantity. Finally, an example is discussed to illustrate these results.

关键词: mechano-electrical system, non-Noether symmetry, non-Noether conserved quantity, infinitesimal transformation

Abstract: This paper focuses on studying non-Noether symmetries and conserved quantities of Lagrange mechano-electrical dynamical systems. Based on the relationships between the motion and Lagrangian, we present conservation laws on non-Noether symmetries for Lagrange mechano-electrical dynamical systems. A criterion is obtained on which non-Noether symmetry leads to Noether symmetry of the systems. The work also gives connections between the non-Noether symmetries and Lie point symmetries, and further obtains Lie invariants to form a complete set of non-Noether conserved quantity. Finally, an example is discussed to illustrate these results.

Key words: mechano-electrical system, non-Noether symmetry, non-Noether conserved quantity, infinitesimal transformation

中图分类号:  (General properties, structure, and representation of Lie groups)

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