中山大学学报自然科学版 ›› 2019, Vol. 58 ›› Issue (5): 44-48.doi: 10.13471/j.cnki.acta.snus.2019.05.007

• 论文 • 上一篇    下一篇

相空间中可控力学系统的Noether对称性与守恒量

季晓慧,朱建青   

  1. 苏州科技大学数理学院,江苏 苏州 215009
  • 收稿日期:2018-08-12 出版日期:2019-09-25 发布日期:2019-09-25
  • 通讯作者: 朱建青(1962年生), 男;研究方向:应用数学;E-mail: zjq@mail.usts.edu.cn

Noether symmetry and conserved quantity of nonholonomic controllable mechanical systems in phase space

JI Xiaohui, ZHU Jianqing   

  1. College of Mathematics and Physics,Suzhou University of Science and Technology, Suzhou 215009,China
  • Received:2018-08-12 Online:2019-09-25 Published:2019-09-25

摘要:

研究时间尺度上相空间中可控力学系统的Noether对称性与守恒量。建立了时间尺度上可控力学系统的Hamiton方程,给出该系统的Noether广义准对称性的定义和判据,并得到广义准对称性相应的Noether守恒量,并举例说明了其结果的应用。

关键词: 时间尺度, 相空间, 可控力学系统, 对称性, 守恒量

Abstract:

This paper mainly investigated Noether symmetry and conserved quantity of nonholonomic controllable mechanical systems in phase space on time scales. The Hamilton equation for nonholonomic controllable mechanical systems on the time scale is established. We offered the definitions and criteria of the generalized Noether quasi-symmetry, and conserved quantities deduced from the generalized Noether quasi-symmetry are obtained. In the end of the paper, an example is given to illustrate the application of the results.

Key words: time scale, phase space, nonholonomic controllable mechanical system, symmetry, conserved quantity

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