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Symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates

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Chinese Physics B 2009年第8期18卷 3145-3149页

作者：吴惠彬梅凤翔 School of Science Beijing Institute of Technology

This paper discusses the symmetry of Lagrangians of holonomic systems in terms of quasi-coordinates. Firstly, the definition and the criterion of the symmetry are given. Secondly, the condition under which there exists a conserved quantity and the form of the conserved quantity are obtained. Finally, an example is shown to illustrate the application of the results.

关键词： quasi-coordinate holonomic system symmetry of Lagrangians conserved quantity

Weak Noether symmetry for nonholonomic systems of non-Chetaev type

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Chinese Physics B 2008年第9期17卷 3175-3179页

作者：解加芳冮铁强梅凤翔 Department of Mechanics Faculty of ScienceBeijing Institute of Technology

Based on the weak Noether symmetry proposed by Mei F X, this paper discusses the weak Noether symmetry for nonholonomic system of non-Chetaev type, and presents expressions of three kinds of conserved quantities by we... 详细信息

关键词： weak Noether symmetry conserved quantity nonholonomic systems of non-Chetaev type

Two Types of New conserved Quantities and Mei Symmetry of Mechanical Systems in Phase Space

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Communications in Theoretical Physics 2007年第12期48卷 993-995页

作者： WANG Peng FANG Jian-Hui DING Ning College of Physics Science and Technology,China University of Petroleum,Dongying 257061,China College of Physics Science and Technology China University of Petroleum Dongying 257061 China

In this paper,two types of new conserved quantities directly deduced by Mei symmetry in phase space arestudied.The conditions under which Mei symmetry can directly lead to the two types of new conserved quantities andthe forms of the two types of new conserved quantities are given.An example is given to illustrate the application ofthe results.

关键词： phase space Mei symmetry conserved quantity

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

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Communications in Theoretical Physics 2007年第7期48卷 23-26页

作者： XIA Li-Li LI Yuan-Cheng College of Physics Science and Technology,China University of Petroleum,Dongying 257061,China College of Physics Science and Technology China University of Petroleum Dongying 257061 China

In this paper,we study the Noether-form invariance of nonholonomic mechanical controllable systems inphase space.Equations of motion of the controllable mechanical systems in phase space are presented.The definitionand the criterion for this system are presented.A new conserved quantity and the Noether conserved quantity deducedfrom the Noether-form invariance are obtained.An example is given to illustrate the application of the results.

关键词： nonholonomic controllable mechanical system phase space Noether-form invariance conserved quantity

Noether Theorem for Generalized Birkhoffian Systems with Time Delay

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Transactions of Nanjing University of Aeronautics and Astronautics 2018年第3期35卷 507-515页

作者： Zhai Xianghua Zhang Yi School of Science Nanjing University of Science and TechnologyNanjing 210094 P.R.China School of Civil Engineering Suzhou University of Science and TechnologySuzhou 215009P.R.China

The Noether symmetries and the conserved quantities for generalized Birkhoffian systems with time delay are studied.Firstly,the generalized Pfaff-Birkhoff principle with time delay is proposed,and the generalized Birkhoff's equations with time delay are obtained.Secondly,the generalized Noether quasi-symmetric transformations of the system are defined,and the criterion of the Noether symmetries is established.Then the Noether theorem for generalized Birkhoffian systems with time delay is established.Finally,by imposing restrictions of constraints on the infinitesimal transformations,the Noether theorem of constrained Birkhoffian systems with time delay is established.One example is given to illustrate the application of the results.

关键词： time delay generalized Birkhoffian system Noether symmetry conserved quantity

Fractional Action-Like Variational Problem and Its Noether Symmetries for a Nonholonomic System

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Transactions of Nanjing University of Aeronautics and Astronautics 2015年第4期32卷 380-389页

作者：张毅龙梓轩 College of Civil Engineering Suzhou University of Science and Technology College of Mathematics and Physics Suzhou University of Science and Technology

For an in-depth study on the symmetric properties for nonholonomic non-conservative mechanical systems,the fractional action-like Noether symmetries and conserved quantities for nonholonomic mechanical systems are studied,based on the fractional action-like approach for dynamics modeling proposed by El-Nabulsi.Firstly,the fractional action-like variational problem is established,and the fractional action-like Lagrange equations of holonomic system and the fractional action-like differential equations of motion with multiplier for nonholonomic system are given;secondly,according to the invariance of fractional action-like Hamilton action under infinitesimal transformations of group,the definitions and criteria of fractional action-like Noether symmetric transformations and quasi-symmetric transformations are put forward;finally,the fractional action-like Noether theorems for both holonomic system and nonholonomic system are established,and the relationship between the fractional action-like Noether symmetry and the conserved quantity is given.

关键词： nonholonomic system fractional action-like variational problem symmetric transformation Noether theorem conserved quantity

Structure properties and Noether symmetries for super-long elastic slender rod

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Chinese Physics B 2008年第7期17卷 2361-2365页

作者：傅景礼赵维加翁玉权 Institute of Mathematical Physics Zhejiang Sci-Tech University Department of Mathematics Qingdao University

DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. This paper studies the structural properties of a super-long elastic slender rod as a structural model of DNA by using Kirchhoff＇s analogue technique and presents the Noether symmetries of the model by using the method of infinitesimal transformation. Baaed on Kirchhoff＇s analogue it analyses the generalized Hamilton canonical equations. The infinitesimal transfornaationa with rcspect to the radial coordinnte, the gonarnlizod coordinates, and the Cluasi-momenta of 5he model are introduced. The Noether gymmetries and conserved qugntities of the model are obtained.

关键词： super-long elastic slender rod Kirchhoff＇s analogue Noether symmetry conserved quantity

A UNIFIED SYMMETRY OF LAGRANGIAN SYSTEMS

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Acta Mechanica Sinica 2004年第6期20卷 668-671页

作者：梅凤翔许学军张永发 Department of Mechanics Beijing Institute of TechnologyBeijing 100081China Department of Mechanics Beijing Institute of TechnologyBeijing 100081China Department of PhysicsZhejiang Normal UniversityJinhua 321004China

In this paper, the definition and the criterion of a unified symmetry are presented. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symm... 详细信息

关键词： analytical mechanics symmetry conserved quantity

THE LIE SYMMETRIES AND conserved QUANTITIES OF VARIABLE-MASS NONHOLONOMIC SYSTEM OF NON-CHETAEV'S TYPE IN PHASE SPACE

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Applied Mathematics and Mechanics(English Edition) 2002年第10期23卷 1215-1220页

作者：方建会赵嵩卿焦志勇 Department of Applied Physics University of Petroleum Shandong P R China

The Lie symmetries and the conserved quantities of a variable mass nonholonomic system of non-Chetaev's type are studied by introducing the infinitesimal transformations of groups in phase space. By using the invariance of the differential equations of motion under the infinitesmal transformations of groups, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equations and the conserved quantities are obtained. An example is given to illustrate the application of the result.

关键词： nonholonomic system phase space analytic mechanics variable mass Lie symmetry conserved quantity