中国物理B ›› 2019, Vol. 28 ›› Issue (12): 120402-120402.doi: 10.1088/1674-1056/ab5210

• GENERAL • 上一篇    下一篇

A new type of adiabatic invariants for disturbednon-conservative nonholonomic system

Xin-Xin Xu(徐鑫鑫), Yi Zhang(张毅)   

  1. 1 College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China;
    2 College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China
  • 收稿日期:2019-07-18 修回日期:2019-09-27 出版日期:2019-12-05 发布日期:2019-12-05
  • 通讯作者: Yi Zhang E-mail:zhy@mail.usts.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11572212, 11272227, and 10972151) and the Innovation Program for Postgraduade in Higher Education Institutions of Jiangsu Province, China (Grant No. KYCX18_2548).

A new type of adiabatic invariants for disturbednon-conservative nonholonomic system

Xin-Xin Xu(徐鑫鑫)1, Yi Zhang(张毅)2   

  1. 1 College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China;
    2 College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China
  • Received:2019-07-18 Revised:2019-09-27 Online:2019-12-05 Published:2019-12-05
  • Contact: Yi Zhang E-mail:zhy@mail.usts.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11572212, 11272227, and 10972151) and the Innovation Program for Postgraduade in Higher Education Institutions of Jiangsu Province, China (Grant No. KYCX18_2548).

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摘要： According to the Herglotz variational principle and differential variational principle of Herglotz type, we study the adiabatic invariants for a non-conservative nonholonomic system. Firstly, the differential equations of motion of the non-conservative nonholonomic system based upon the generalized variational principle of Herglotz type are given, and the exact invariant for the non-conservative nonholonomic system is introduced. Secondly, a new type of adiabatic invariant for the system under the action of a small perturbation is obtained. Thirdly, the inverse theorem of the adiabatic invariant is given. Finally, an example is given.

关键词: non-conservative nonholonomic mechanics, adiabatic invariants, differential variational principle of Herglotz type

Abstract: According to the Herglotz variational principle and differential variational principle of Herglotz type, we study the adiabatic invariants for a non-conservative nonholonomic system. Firstly, the differential equations of motion of the non-conservative nonholonomic system based upon the generalized variational principle of Herglotz type are given, and the exact invariant for the non-conservative nonholonomic system is introduced. Secondly, a new type of adiabatic invariant for the system under the action of a small perturbation is obtained. Thirdly, the inverse theorem of the adiabatic invariant is given. Finally, an example is given.

Key words: non-conservative nonholonomic mechanics, adiabatic invariants, differential variational principle of Herglotz type

中图分类号:  (Canonical formalism, Lagrangians, and variational principles)

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