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A new type of adiabatic invariants for disturbed non-conservative nonholonomic system

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Chinese Physics B 2019年第12期28卷 118-122页

作者： Xin-Xin Xu Yi Zhang College of Mathematics and Physics Suzhou University of Science and TechnologySuzhou 215009China College of Civil Engineering Suzhou University of Science and TechnologySuzhou 215011China

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

Perturbation of Symmetries and Mei adiabatic invariants of Nonholonomic Systems with Servoconstraints

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Communications in Theoretical Physics 2008年第10期50卷 855-860页

作者： XIA Li-Li LI Yuan-Cheng ZHAO Xian-Lin Department of Physics Henan Institute of Education Zhengzhou 450014 China College of Physics Science and Technology China University of Petroleum Dongying 257061 China

The perturbation of symmetries and Mei adiabatic invariants of nonholonomic systems with servoconstraints are studied. The exact invariants in the form of Mei conserved quantities introduced by the Mei symmetry of nonholonomic systems with servoconstraints without perturbations are given. Based on the definition of higher-order adiabatic invariants of mechanical systems, the perturbation of Mei symmetries for nonholonomic .systems with servoconstraints under the action of small disturbance is investigated, and Mei adiabatic invatiants of the system are obtained. An example is given to illustrate the application of the results.

关键词： nonholonomic systems servoconstraints Mei symmetry perturbations adiabatic invariants

Perturbation to Noether Symmetry and adiabatic invariants for Dynamical Systems with Nonstandard Lagrangians

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Journal of Donghua University(English Edition) 2018年第1期35卷 24-27页

作者： WANG Xueping ZHANG Yi College of Mathematics and Physics Suzhou University of Science and TechnologySuzhou 215009China College of Civil Engineering Suzhou University of Science and TechnologySuzhou 215011China

The perturbation to Noether symmetry and adiabatic invariants for dynamical systems with nonstandard Lagrangians are *** on two kinds of nonstandard Lagrangians(*** Lagrangians and power-law Lagrangians),the exact invariants of Noether type are *** on the definition of highorder adiabatic invariants,the relationship between the perturbation of Noether symmetry and the adiabatic invariants of the system under a small disturbance is studied,and then the corresponding theorems of adiabatic invariants are ***,two examples are given to illustrate the methods and results appear in this paper.

关键词： nonstandard Lagrangians Noether symmetry perturbation adiabatic invariants

Perturbation to Symmetry and adiabatic invariants of discrete nonholonomic nonconservative mechanical system

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Perturbation to Symmetry and adiabatic invariants of discret...

Invariant and energy analysis of an axially retracting beam

第九届全国动力学与控制学术会议

作者： Wang Peng College of physics and Electronic Engineering Xinjiang Normal University Shanghai Institute of Applied Mathematics and Mechanics Shanghai University

Symmetry and conserved quantities of mechanical system are of important *** of difference equations and discrete mechanical system are extensively investigated in recent *** are mainly two opinions about this *** possibility is to consider the difference equations on a fixed lattice and consider only transformations that do not act on the *** second possibility is to consider group transformations acting both on the difference equations and on the

关键词： symmetry perturbation adiabatic invariants discrete mechanical system

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Chinese Journal of Aeronautics 2016年第4期29卷 952-961页

作者： Yang Xiaodong Liu Ming Zhang Wei Roderick V.N.Melnik Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Engineering College of Mechanical Engineering Beijing University of Technology M2NeT Laboratory The MS2Discovery Interdisciplinary Research Institute Wilfrid Laurier University

The mechanism of a retracting cantilevered beam has been investigated by the invariant and energy-based analysis. The time-varying parameter partial differential equation governing the transverse vibrations of a beam with retracting motion is derived based on the momentum theorem. The assumed-mode method is used to truncate the governing partial differential equation into a set of ordinary differential equations (ODEs) with time-dependent coefficients. It is found that if the order of truncation is not less than the order of the initial conditions, the assumed-mode method can yield accurate results. The energy transfers among assumed modes are discussed during retraction. The total energy varying with time has been investigated by numerical and analytical methods, and the results have good agreement with each other. For the transverse vibrations of the axially retracting beam, the adiabatic invariant is derived by both the averaging method and the Bessel function method. (C) 2016 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license.

关键词： adiabatic invariants Asymptotic analysis Retracting beam Time-varying systems Transient dynamics