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

doi:10.1088/1674-1056/ab5210

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.

Keywords: non-conservative nonholonomic mechanics adiabatic invariants differential variational principle of Herglotz type

Received: 18 July 2019
Revised: 27 September 2019
Accepted manuscript online:

PACS:

04.20.Fy

(Canonical formalism, Lagrangians, and variational principles)

Fund: 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).

Corresponding Authors: Yi Zhang
E-mail: zhy@mail.usts.edu.cn

Cite this article:

Xin-Xin Xu(徐鑫鑫), Yi Zhang(张毅) A new type of adiabatic invariants for disturbednon-conservative nonholonomic system 2019 Chin. Phys. B 28 120402

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

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