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non-noether conserved quantity for Relativistic nonholonomic System with Variable Mass

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Communications in Theoretical Physics 2005年第2期43卷 197-200页

作者： QIAOYong-Fen LIRen-Jie MAYong-Sheng DepartmentofMechanicalEngineeringandAutomation ZhejiangInstituteofScienceandTechnologyHangzhou312207China／／FacultyofScienceLaiyangAgriculturalCollegeLaiyang265200China FacultyofScience LaiyangAgriculturalCollegeLaiyang265200China EngineeringCollege NortheastAgriculturalUniversityHarbin150030China

Using form invariance under special infinitesimal transformations in which time is not variable, the non-noether conserved quantity of the relativistic nonholonomic system with variable mass is studied. The differential equations of motion of the system are established. The definition and criterion of the form invariance of the system under infinitesimal transformations are studied. The necessary and sufficient. condition under which the form invariance is a Lie symmetry is given. The condition under which the form invariance can be led to a non-noether. 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 relativity nonholonomic system variable mass non-noether conserved quantity

non-noether conserved quantity constructed by using form invariance for Birkhoffian system

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Chinese Physics B 2004年第12期13卷 1999-2002页

作者：许学军梅凤翔秦茂昌 DepartmentofMechanics BeijingInstituteofTechnologyBeijing100081China//DepartmentofPhysicsZhejiangNormalUniversityJinhua321004China DepartmentofMechanics BeijingInstituteofTechnologyBeijing100081China

Based on the invariance of Birkhoffian equations under the infinitesimal transformations of groups, the definition and the criterion of a form invariance for a Birkhoffian system are established. The condition under which the form invariance can lead to a non-noether conserved quantity and the form of the conserved quantity are deduced by relying on the total time derivative along the trajectory of the equations, and two corollaries in special cases are presented. An example is finally given to illustrate the application of the results.

关键词： Birkhoffian system form invariance non-noether conserved quantity

A set of Lie symmetrical non－noether conserved quantity for the relativistic Hamiltonian systems

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Chinese Physics B 2003年第8期12卷 841-845页

作者：罗绍凯贾利群蔡建乐 InstituteofMathematicalMechanicsandMathematicalPhysics ChangshaUniversityChangsha410003China ScienceCollegeofSouthern YangtzeUniversityWuxi214063China DepartmentofPhysics HunanUniversityChangsha410082China

For the relativistic Hamiltonian system, a new type of Lie symmetrical non-noether conserved quantities are *** the basis of the theory of invariance of differential equations under infinitesimal transformations, and introducing special infinitesimal transformations for qs and Ps, we construct the determining equations of Lie symmetrical transformations of the system, which only depend on the canonical variables. A set of non-noether conserved quantities are directly obtained from the Lie symmetries of the system. An example is given to illustrate the application of the results.

关键词： relativity Hamiltonian system Lie symmetry non-noether conserved quantity

The Lie symmetrical non-noether conserved quantity of holonomic Hamiltonian system

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Chinese Physics B 2004年第10期13卷 1620-1622页

作者：方建会廖永潘彭勇 CollegeofPhysicsScienceandTechnology UniversityofPetroleumDongying257061China DepartmentofPhysics HexiCollegeZhangye734000China

In this paper, we study the Lie symmetrical non-noether conserved quantity of a holonomic Hamiltonian system under the general infinitesimal transformations of groups. Firstly, we establish the determining equations of Lie symmetry of the system. Secondly, the Lie symmetrical non-noether conserved quantity of the system is deduced. Finally,an example is given to illustrate the application of the result.

关键词： Hamiltonian system Lie symmetry non-noether conserved quantity

A new type of Lie symmetrical non-noether conserved quantity for nonholonomic systems

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Chinese Physics B 2004年第12期13卷 2182-2186页

作者：罗绍凯黄飞江卢一兵 InstituteofMathematicalMechanicsandMathematicalPhysics ZhejiangUniversityofSciencesHangzhou310018China//InstituteofMathematicalMechanicsandMathematicalPhysicsChangshaUniversityChangsha410003China InstituteofMathematicalMechanicsandMathematicalPhysics ChangshaUniversityChangsha410003China

For a nonholonomic system, a new type of Lie symmetrical non-noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the invariance theory of differential equations of motion under infinitesimal transformations for t and qs, we construct the Lie symmetrical determining equations, the constrained restriction equations and the additional restriction equations of the system. And a new type of Lie symmetrical non-noether conserved quantity is directly obtained from the Lie symmetry of the system, which only depends on the variables t, qs and qs. A series of deductions are inferred for a holonomic nonconservative system,Lagrangian system and other dynamical systems in the case of vanishing of time variation. An example is given to illustrate the application of the results.

关键词： nonholonomic system Lie symmetry non-noether conserved quantity

Mei Symmetry and Hojman conserved quantity of nonholonomic Controllable Mechanical System

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Communications in Theoretical Physics 2008年第8期50卷 331-334页

作者： XIA Li-Li LIYuan-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

A non-noether conserved quantity, i.e., Hojman conserved quantity, constructed by using Mei symmetry for the nonholonomic controllable mechanical system, is presented. Under general infinitesimal transformations, the determining equations of the special Mei symmetry, the constrained restriction equations, the additional restriction equations, and the definitions of the weak Mei symmetry and the strong Mei symmetry of the nonholonomic controllable mechanical system are given. The condition under which Mei symmetry is a Lie symmetry is obtained. The form of the Hojman conserved quantity of the corresponding holonomic mechanical system, the weak Hojman conserved quantity and the strong Hojman conserved quantity of the nonholonomie controllable mechanical system are obtained. An example is given to illustrate the application of the results.

关键词： nonholonomic controllable mechanical system non-noether conserved quantity Hojman con-served quantity

Weak noether Symmetry and non-noether conserved Quantities for General Holonomic Systems

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Communications in Theoretical Physics 2008年第10期50卷 844-846页

作者： XIE Jia-Fang MEI Feng-Xiang GANG Tie-Qiang Department of Mechanics Beijing Institute of Technology Beijing 100081 China

A new kind of weak noether symmetry for a general holonomic system is defined in such a way that themethods to construct Hojman conserved quantity and new-type conserved quantity are *** turns out that weintroduce a n... 详细信息

关键词： weak noether symmetry non-noether conserved quantity general holonomic system

Lie Symmetrical non-noether conserved Quantities of Poincaré-Chetaev Equations

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Communications in Theoretical Physics 2005年第2X期44卷 223-225页

作者： ZHANG Peng-Yu FANG Jian-Hui College of Physics and Technology China University of Petroleum Dongying 257061 China

In the present paper the Lie symmetrical non-noether conserved quantity of the Poincaré-Chetaev equations under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-noether conserved quantity of the equations is deduced.

关键词： Poincaré-Chetaev equations Lie symmetry non-noether conserved quantity

non-noether symmetries and conserved quantities of the Lagrange mechano-electrical systems

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Chinese Physics B 2004年第11期13卷 1784-1789页

作者：傅景礼陈立群刘荣万 DepartmentofAppliedPhysics ZhejiangUniversityofScienceHangzhou310018China DepartmentofMechanics ShanghaiUniversityShanghai200072China ShanghaiInstituteofAppliedMathematicsandMechanics ShanghaiUniversityShanghai200072China

This paper focuses on studying non-noether symmetries and conserved quantities of Lagrange mechano-electrical dynamical systems. Based on the relationships between the motion and Lagrangian, we present conservation laws on non-noether symmetries for Lagrange mechano-electrical dynamical systems. A criterion is obtained on which non-noether symmetry leads to noether symmetry of the systems. The work also gives connections between the nonnoether symmetries and Lie point symmetries, and further obtains Lie invariants to form a complete set of non-noether conserved quantity. Finally, an example is discussed to illustrate these results.

关键词： mechano-electrical system non-noether symmetry non-noether conserved quantity in finitesimal transformation