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Chinese Physics B 2014年第10期23卷 292-298页

作者：张相武李院院赵小侠罗文峰 School of Physics and Mechatronic Engineering Xi’an University of Arts and Science School of Electronic Engineering Xi’an University of Posts and Telecommunications

In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d＇Alembert principle of the system, the higher-order velocity energy and the higher-order acceleration energy of the system in event space are defined, the higher-order d＇Alembert- Lagrange principle of the system in event space is established, and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the higher-order differential equations of motion for holonomic systems in event space are obtained.

关键词： event space the higher-order d'Alembert-Lagrange principle the higher-order time rate of changeof force the higher-order differential equations of motion

Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space

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Chinese Physics B 2009年第11期18卷 4636-4642页

作者：张毅 College of Civil Engineering Suzhou University of Science and Technology

This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.

关键词： holonomic system conformal invariance symmetry event space

Symmetry of the Lagrangians of holonomic nonconservative system in event space

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Chinese Physics B 2012年第7期21卷 61-65页

作者：张斌方建会张伟伟 College of Science China University of Petroleum(East China)

This paper analyzes the symmetry of Lagrangians and the conserved quantity for the holonomic non-conservative system in the event space. The criterion and the definition of the symmetry are proposed first, then a quantity caused by the symmetry and its existence condition are given. An example is shown to illustrate the application of the result at the end.

关键词： symmetry of Lagrangians event space holonomic nonconservative system conservedquantity

Poisson theory and integration method of Birkhoffian systems in the event space

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Chinese Physics B 2010年第8期19卷 80-84页

作者：张毅 College of Civil Engineering Suzhou University of Science and Technology

This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff＇s equations in the event space are given. The Poisson theory of the Birkhoffian system in the event space is established. The definition of the Jacobi last multiplier of the system is given, and the relation between the Jacobi last multiplier and the first integrals of the system is discussed. The researches show that for a Birkhoffian system in the event space, whose configuration is determined by （2n ＋ 1） Birkhoff＇s variables, the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known. An example is given to illustrate the application of the results.

关键词： Birkhoffian system event space method of integration Jacobi last multiplier

Routh method of reduction for Birkhoffian systems in the event space

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Chinese Physics B 2008年第12期17卷 4365-4368页

作者：张毅 College of Civil Engineering Suzhou University of Science and Technology

For a Birkhoffian system in the event space, this paper presents the Routh method of reduction. The parametric equations of the Birkhoffian system in the event space are established, and the definition of cyclic coordinates for the system is given and the corresponding cyclic integral is obtained. Through the cyclic integral, the order of the system can be reduced. The Routh functions for the Birkhoffian system in the event space are constructed, and the Routh method of reduction is successfully generalized to the Birkhoffian system in the event space. The results show that if the system has a cyclic integral, then the parametric equations of the system can be reduced at least by two degrees and the form of the equations holds. An example is given to illustrate the application of the results.

关键词： event space Birkhoffian system reduction cyclic integral

Unified Symmetry of Nonholonomic System of Non-Chetaev＇s Type in event space

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Communications in Theoretical Physics 2007年第2期47卷 221-224页

作者： HOU Qi-Bao LI Yuan-Cheng WANG Jing XIA Li-Li College of Physics Science and Technology China University of Petroleum Dongying 257061 China

The unified symmetry of a nonholonomic system of non-Chetaev＇s type in event space under infinitesimal transformations of group is studied. Firstly, the differential equations of motion of the system are given. Secondly, the definition and the criterion of the unified symmetry for the system are obtained. Thirdly, a new conserved quantity, besides the Noether conserved quantity and the Hojman conserved quantity, is deduced from the unified symmetry of a nonholonomic system of non-Chetaev＇s type. Finally, an example is given to illustrate the application of the result.

关键词： event space nonholonomic system unified symmetry conserved quantity

A General Approach to the Construction of Conservation Laws for Birkhoffian Systems in event space

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Communications in Theoretical Physics 2008年第10期50卷 851-854页

作者： ZHANG Yi College of Civil Engineering Suzhou University of Science and Technology Suzhou 215011 China

For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the parametric equations of the system. First, the parametric equations of the Birkhoffian system in the event space are established, and the definition of integrating factors for the system is given; second the necessary conditions for the existence of conservation laws are studied in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the results.

关键词： event space Birkhoffian system integrating factor conservation theorem Killing equation

Unified Symmetry of Nonholonomic System of Non-Chetaev＇s Type with Variable Mass in event space

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Communications in Theoretical Physics 2007年第4X期48卷 619-622页

作者： HOU Qi-Bao LI Yuan-Cheng XiA Li-Li WANG Jing College of Physics Science and Technology China University of Petroleum Dongying 257061 China

The unified symmetry of a nonholonomic system of non-Chetaev＇s type with variable mass in event space is studied. The differential equations of motion of the system are given. Then the definition and the criterion of the unified symmetry for the system are obtained. Finally, the Noether conserved quantity, the Hojman conserved quantity, and a new type of conserved quantity are deduced from the unified symmetry of the nonholonomic system of non-Chetaev＇s type with variable mass in event space at one time. An example is given to illustrate the application of the results.

关键词： event space nonholonomic system variable mass unified symmetry conserved quantity

Lie-Form Invariance of the Nonholonomic System of Relative Motion in event space

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Communications in Theoretical Physics 2007年第5X期48卷 795-798页

作者： HOU Qi-Bao LI Yuan-Cheng WANG Jing XIA Li-Li College of Physics Science and Technology China University of Petroleum Dongying 257061 China

In this paper, the Lie-form invariance of a nonholonomic system of relative motion in event space is studied. Firstly, the definition and the criterion of the Lie-form invariance of the nonholonomic system of relative motion in event space is given. Secondly, the Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. An example is given to illustrate the application of the results.

关键词： event space nonholonomic system relative motion Lie-form invariance conserved quantity

Hojman Conserved Quantities for Birkhoffian Systems in event space

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Communications in Theoretical Physics 2008年第7期50卷 59-62页

作者： ZHANG Yi College of Civil Engineering Suzhou University of Science and Technology Suzhou 215011 China

This paper focuses on studying a Hojman conserved quantity directly derived from a Lie symmetry fora Birkhoffian system in the event *** Birkhoffian parametric equations for the system are established,and thedetermining equations of Lie symmetry for the system are *** conditions under which a Lie symmetry ofBirkhoffian system in the event space can directly lead up to a Hojman conserved quantity and the form of the Hojmanconserved quantity are *** example is given to illustrate the application of the results.

关键词： event space Birkhoffian system Lie symmetry Hojman conserved quantity