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Mei’s symmetry theorem for time scales nonshifted mechanical systems

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Theoretical & Applied Mechanics Letters 2021年第5期11卷 246-251页

作者： Yi Zhang College of Civil Engineering Suzhou University of Science and TechnologySuzhou 215011China

We focus on Mei symmetry for time scales nonshifted mechanical systems within Lagrangian framework and its resulting new conserved ***,the dynamic equations of time scales nonshifted holonomic systems and time scales nonshifted nonholonomic systems are derived from the generalized Hamilton’s ***,the definitions of Mei symmetry on time scales are given and its criterions are ***,Mei’s symmetry theorems for time scales nonshifted holonomic conservative systems,time scales nonshifted holonomic nonconservative systems and time scales nonshifted nonholonomic systems are established and proved,and new conserved quantities of above systems are *** are illustrated with two examples.

关键词： Mei’s symmetry theorem nonholonomic system Nonconservative system Time scales Nonshifted calculus of variation

FORMULATION AND SOLUTION FOR INVERSE PROBLEM OF nonholonomic DYNAMICS

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Applied Mathematics and Mechanics(English Edition) 1993年第4期14卷 327-332页

作者：刘凤丽梅凤翔 Liaoning University Shenyang Peking Institute of Technology Beijing

This paper presents a formulation and solution for the inverse problem of nonholonomic dynamics: to find the form of nonholonomic constraints when some integrals are given and to find the generalized reactive forces of constraint acting on the system when the expression of the kinetic energy is given. An example is given to illustrate the application of the result.

关键词： analytical mechanics nonholonomic system integral inverse problem

ON　THE　STABILITY　OF　nonholonomic　MECHANICAL　systemS　WITH　RESPECT　TO　PARTIAL　VARIABLES

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Applied Mathematics and Mechanics(English Edition) 1995年第3期16卷 237-245页

作者：朱海平梅凤翔 Beijing University of Science and Technology Beijing

In this paper. a method to study the stability of nonholonomic systems withrespect to partial variables is given and several stability theorems of nonholonomicsystems with respect to partial variables are obtained. Moreover, a relationshipbetween the stability of a nonholonomic system with respect to all variables and thatto partial variables is obtained.

关键词： nonholonomic system stability with respect to partial variables,constraint manifold

Lie Symmetries and Conserved Quantities of Arbitrary Order nonholonomic systems

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Journal of Beijing Institute of Technology 2000年第2期9卷 131-137页

作者：赵树信尚玫梅凤翔北京理工大学应用力学系北京100081

The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, th... 详细信息

关键词： nonholonomic system determining equations restriction equations structure equation conserved quantities

GIBBS-APPELL’S EQUATIONS OF VARIABLE MASS NONLINEAR nonholonomic MECHANICAL systemS

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Applied Mathematics and Mechanics(English Edition) 1990年第10期11卷 973-983页

作者：乔永芬 1. Northeast Agricultural College Harbin

In this paper, the Gibbs-Appell's equations of motion are extended to the most general variable mass nonholonomie mechanical systems. Then the Gibbs-Appell's equations of motion in terms of generalized coordinates or quasi-coordinates and an integral variational principle of variable mass nonlinear nonholonomie mechanical systems are obtained. Finally, an example is given.

关键词： variable mass nonholonomic system Gibbs-Appell's equation integral variational principle quasi-velocity

Potential method of integration for solving the equations of mechanical systems

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Chinese Physics B 2006年第5期15卷 899-902页

作者：吴惠彬 Faculty of Science Beijing Institute of Technology Beijing 100081 China

This paper is intended to apply a potential method of integration to solving the equations of holonomic and nonholonomic systems. For a holonomic system, the differential equations of motion can be written as a system of differential equations of first order and its fundamental partial differential equation is solved by using the potential method of integration. For a nonholonomic system, the equations of the corresponding holonomic system are solved by using the method and then the restriction of the nonholonomic constraints on the initial conditions of motion is added.

关键词： potential method of integration holonomic system nonholonomic system equation of motion

Existential theorem of conserved quantities and its inverse for the dynamics of nonholonomic relativistic systems

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Chinese Physics B 2002年第9期11卷 859-863页

作者：乔永芬孟军等 EngineeringCollege NortheastAgriculturalUniversityHarbin150030China

We present a general approach to the construction of conservation laws for the dynamics of nonholonomic rel-ativistic systems. Firstly, we give the definition of integrating factors for the differential equations of motion of amechanical system. Next, the necessary conditions for the existence of the conserved quantities are studied in ***, we establish the existential theorem for the conserved quantities and its inverse for the equations of motion of anonholonomic relativistic system. Finally, an example is given to illustrate the application of the result.

关键词： nonholonomic system relativity integrating factor conserved theorem

Conserved quantities from Lie symmetries for nonholonomic systems

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Journal of Southeast University(English Edition) 2003年第3期19卷 289-292页

作者：张毅薛纭苏州科技学院土木工程系苏州215011 上海应用技术学院机械工程系上海200233

This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.

关键词： analytical mechanics nonholonomic system symmetry conserved quantity

Modeling and adaptive motion/force tracking for vertical wheel on rotating table

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Journal of systems Science & Complexity 2015年第5期28卷 1060-1069页

作者： Zhongcai Zhang Yuqiang Wu Wei Sun School of Automation Southeast University Institute of Automation Qufu Normal University

This paper is devoted to the problem of modeling and adaptive motion/force tracking for a class of nonholonomic dynamic systems with affine constraints(NDSAC): a vertical wheel on a rotating table. Prior to the development of tracking controller,the dynamic model of the wheel in question is derived in a meticulous manner. A continuously differentiable friction model is also considered in the modeling. By exploiting the inherent cascade interconnected structure of the wheel dynamics, an adaptive motion/force tracking controller is presented guaranteeing that the trajectory tracking errors asymptotically converge to zero while the contact force tracking errors can be made small enough by tuning design parameters. Simulation results are provided to validate the effectiveness of the proposed tracking methodology.

关键词： nonholonomic system adaptive motion/force tracking mechanics model affine constraint.