中国物理B ›› 2004, Vol. 13 ›› Issue (3): 287-291.doi: 10.1088/1009-1963/13/3/004

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Velocity-dependent symmetries and conserved quantities of the constrained dynamical systems

傅景礼1, 陈立群2, 杨晓东2   

  1. (1)Institute of Mathematical Mechanics and Mathematical Physics of Shangqiu Teachers College, China; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; (2)Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • 收稿日期:2003-05-28 修回日期:2003-10-13 出版日期:2004-03-06 发布日期:2005-07-06
  • 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, China (Grant No 0311011400).

Velocity-dependent symmetries and conserved quantities of the constrained dynamical systems

Fu Jing-Li (傅景礼)ab, Chen Li-Qun (陈立群)b, Yang Xiao-Dong (杨晓东)b   

  1. a Institute of Mathematical Mechanics and Mathematical Physics of Shangqiu Teachers College, China; b Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • Received:2003-05-28 Revised:2003-10-13 Online:2004-03-06 Published:2005-07-06
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10372053) and the Natural Science Foundation of Henan Province, China (Grant No 0311011400).

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摘要： In this paper, we have extended the theorem of the velocity-dependent symmetries to nonholonomic dynamical systems. Based on the infinitesimal transformations with respect to the coordinates, we establish the determining equations and restrictive equation of the velocity-dependent system before the structure equation is obtained. The direct and the inverse issues of the velocity-dependent symmetries for the nonholonomic dynamical system is studied and the non-Noether type conserved quantity is found as the result. Finally, we give an example to illustrate the conclusion.

关键词: velocity-dependent symmetry, Lie group, determining equation, non-Noether type conserved quantity

Abstract: In this paper, we have extended the theorem of the velocity-dependent symmetries to nonholonomic dynamical systems. Based on the infinitesimal transformations with respect to the coordinates, we establish the determining equations and restrictive equation of the velocity-dependent system before the structure equation is obtained. The direct and the inverse issues of the velocity-dependent symmetries for the nonholonomic dynamical system is studied and the non-Noether type conserved quantity is found as the result. Finally, we give an example to illustrate the conclusion.

Key words: velocity-dependent symmetry, Lie group, determining equation, non-Noether type conserved quantity

中图分类号:  (Inverse problems)

  • 02.30.Zz
02.20.Sv (Lie algebras of Lie groups)