中国物理B ›› 2003, Vol. 12 ›› Issue (7): 695-699.doi: 10.1088/1009-1963/12/7/301

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Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems

白景华1, 傅景礼2, 陈立群3, 杨晓东3   

  1. (1)Department of Mathematics, Kaifeng University, Kaifeng 475000, China; (2)Institute of Mathematical Mechanics and Mathematical Physics, Shangqiu Teachers College, Shangqiu 476000, 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
  • 收稿日期:2002-09-06 修回日期:2003-03-12 出版日期:2003-07-16 发布日期:2005-03-16

Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems

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

  1. a Institute of Mathematical Mechanics and Mathematical Physics, Shangqiu Teachers College, Shangqiu 476000, China; b Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; Department of Mathematics, Kaifeng University, Kaifeng 475000, China
  • Received:2002-09-06 Revised:2003-03-12 Online:2003-07-16 Published:2005-03-16

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摘要： This paper concentrates on studying the Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems. Based on the infinitesimal transformation, we establish the Lie symmetric determining equations and restrictive equations and give three definitions of Lie symmetries before the structure equations and conserved quantities of the Lie symmetries are obtained. Then we make a study of the inverse problems. Finally, an example is presented for illustrating the results.

Abstract: This paper concentrates on studying the Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems. Based on the infinitesimal transformation, we establish the Lie symmetric determining equations and restrictive equations and give three definitions of Lie symmetries before the structure equations and conserved quantities of the Lie symmetries are obtained. Then we make a study of the inverse problems. Finally, an example is presented for illustrating the results.

Key words: control, nonholonomic dynamical systems, Lie symmetry, conserved law

中图分类号:  (Ordinary differential equations)

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