中山大学学报自然科学版 ›› 2018, Vol. 57 ›› Issue (2): 76-79.

• 论文 • 上一篇    下一篇

时间尺度上非Chetaev型非完整系统的Lie对称性及其守恒量

林魏,朱建青   

  1. 苏州科技大学数理学院,江苏 苏州 215009
  • 收稿日期:2017-06-26 出版日期:2018-03-25 发布日期:2018-03-25

The Lie symmetry and conserved quantity for nonholonomic systems of non-Chetaev's type on time scales

LIN Wei, ZHU Jianqing   

  1. College of Mathematics and Physics, Jiangsu University of Science and Technology, Suzhou 215009,China
  • Received:2017-06-26 Online:2018-03-25 Published:2018-03-25

摘要:

研究了时间尺度上非Chetaev型非完整系统的Lie对称性及其守恒量。首先,给出了时间尺度上非Chetaev型非完整系统的运动微分方程;然后,基于微分方程在无限小变换下的不变性,得到了确定方程,给出了非Chetaev型非完整系统下的限制方程,进而建立了时间尺度上非Chetaev型非完整系统的Lie对称性及其守恒量;最后,举例说明其结果的应用。

关键词: 时间尺度, 非Chetaev型, 非完整系统, Lie对称性, 守恒量

Abstract:

The Lie symmetry and conserved quantity for nonholonomic systems of non-Chetaev's type on time scales are studied. Firstly, the differential equations of motion for nonholonomic systems of non-Chetaev's type on time scales are given. Secondly, based on the invariance of differential equation under the infinitesimal transformations, the determinating equation is established and the restriction equations for nonholonomic systems of non-Chetaev's type are given. Then, the Lie theorem and conserved quantity for nonholonomic systems of non-Chetaev's type on time scales are built. Finally, an example is given to illustrate the application of the results.

Key words: time scales, non-Chetaev's type, nonholonomic systems, Lie symmetry, conserved quantity

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