中国物理B ›› 2006, Vol. 15 ›› Issue (2): 243-248.doi: 10.1088/1009-1963/15/2/001

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Non-Noether symmetries and Lutzky conservative quantities of nonholonomic nonconservative dynamical systems

郑世旺1, 唐贻发1, 傅景礼2   

  1. (1)Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China; (2)State Key Laboratory of Scientific and Engineering Computing,Chinese Academy of Sciences 100080, China;Department of Physics, Zhejiang Science and Technology University,Hangzhou 310018, China;Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China
  • 收稿日期:2005-05-26 修回日期:2005-09-14 出版日期:2006-02-20 发布日期:2006-02-20
  • 基金资助:
    Project supported by the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences and the National Natural Science Foundation of China (Grant No 10372053) and the Natural Science Foundation of Henan Province Government, China (Grant Nos 0311011400, 0511022200).

Non-Noether symmetries and Lutzky conservative quantities of nonholonomic nonconservative dynamical systems

Zheng Shi-Wang (郑世旺)a, Tang Yi-Fa (唐贻发)a, Fu Jing-Li (傅景礼)bcd   

  1. a Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China; b State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences 100080, Chinac Department of Physics, Zhejiang Science and Technology University, Hangzhou 310018, Chinad Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China
  • Received:2005-05-26 Revised:2005-09-14 Online:2006-02-20 Published:2006-02-20
  • Supported by:
    Project supported by the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences and the National Natural Science Foundation of China (Grant No 10372053) and the Natural Science Foundation of Henan Province Government, China (Grant Nos 0311011400, 0511022200).

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摘要： Non-Noether symmetries and conservative quantities of nonholonomic nonconservative dynamical systems are investigated in this paper. Based on the relationships among motion, nonconservative forces, nonholonomic constrained forces and Lagrangian, non-Noether symmetries and Lutzky conservative quantities are presented for nonholonomic nonconservative dynamical systems. The relation between non-Noether symmetry and Noether symmetry is discussed and it is further shown that non-Noether conservative quantities can be obtained by a complete set of Noether invariants. Finally,an example is given to illustrate these results.

关键词: conserved quantity, non-Noether symmetry, nonholonomic nonconservative system, in finitesimal transformation

Abstract: Non-Noether symmetries and conservative quantities of nonholonomic nonconservative dynamical systems are investigated in this paper. Based on the relationships among motion, nonconservative forces, nonholonomic constrained forces and Lagrangian, non-Noether symmetries and Lutzky conservative quantities are presented for nonholonomic nonconservative dynamical systems. The relation between non-Noether symmetry and Noether symmetry is discussed and it is further shown that non-Noether conservative quantities can be obtained by a complete set of Noether invariants. Finally,an example is given to illustrate these results.

Key words: conserved quantity, non-Noether symmetry, nonholonomic nonconservative system, in finitesimal transformation

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
02.30.Jr (Partial differential equations)