中国物理B ›› 2001, Vol. 10 ›› Issue (3): 181-185.doi: 10.1088/1009-1963/10/3/302

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SYMMETRIES OF MECHANICAL SYSTEMS WITH NONLINEAR NONHOLONOMIC CONSTRAINTS

姜丽妍1, 郭永新2, 于莹3   

  1. (1)Department of Electronics and Information Engineering, Dandong Advanced Academy, Dandong 118000, China; (2)Department of Physics, Liaoning University, Shenyang 110036, China; (3)School of Science, Shenyang University of Technology, Shenyang 110023, China
  • 收稿日期:2000-09-21 修回日期:2000-11-21 出版日期:2001-03-15 发布日期:2005-06-12
  • 基金资助:
    Supported by the Natural Science Foundation of Liaoning Province of China and the Science Research Foundation of Provincial Education Committee of Liaoning, China (Grant No.990111004, 20021004).

SYMMETRIES OF MECHANICAL SYSTEMS WITH NONLINEAR NONHOLONOMIC CONSTRAINTS

Guo Yong-xin (郭永新)a, Jiang Li-yan (姜丽妍)b, Yu Ying (于莹)c   

  1. a Department of Physics, Liaoning University, Shenyang 110036, China; b Department of Electronics and Information Engineering, Dandong Advanced Academy, Dandong 118000, China; c School of Science, Shenyang University of Technology, Shenyang 110023, China
  • Received:2000-09-21 Revised:2000-11-21 Online:2001-03-15 Published:2005-06-12
  • Supported by:
    Supported by the Natural Science Foundation of Liaoning Province of China and the Science Research Foundation of Provincial Education Committee of Liaoning, China (Grant No.990111004, 20021004).

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摘要： The dynamical symmetries and adjoint symmetries of nonlinear nonholonomic constrained mechanical systems are analysed in two kinds of geometrical frameworks whose evolution equations are Routh's equations and generalized Chaplygin's equations, respectively. The Lagrangian inverse problem and the interrelation between Noether's symmetries and dynamical symmetries are briefly concerned with. Finally an illustrative example is analysed.

Abstract: The dynamical symmetries and adjoint symmetries of nonlinear nonholonomic constrained mechanical systems are analysed in two kinds of geometrical frameworks whose evolution equations are Routh's equations and generalized Chaplygin's equations, respectively. The Lagrangian inverse problem and the interrelation between Noether's symmetries and dynamical symmetries are briefly concerned with. Finally an illustrative example is analysed.

Key words: nonholonomic constraints, dynamical symmetries, adjoint symmetries, Noether symmetries

中图分类号:  (Nonlinear and dynamical symmetries (spectrum-generating symmetries))

  • 11.30.Na
02.30.Zz (Inverse problems)