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lie Symmetry and Conserved Quantities for Mechanical-Electrical Systems

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Communications in Theoretical Physics 2008年第6期49卷 1417-1420页

作者： JING Hong-Xing li yuan-cheng College of Physics Science and Technology China University of Petroleum （East China） Dongying 257061 China

In this paper, we study lie symmetry and conserved quantities for a mechanical-electrical system. The criterion of the lie symmetry for this system is given. The generalized Hojman conserved quantity and generalized Lutzky conserved quantity deduced from the lie symmetry for the system are obtained. An example is presented to illustrate the results.

关键词： mechanical-electrical system lie symmetry generalized Hojman conserved quantity, generalized Lutzky conserved quantity

Mei Symmetry and Lutzky Conserved Quantity for Nonholonomic Mechanical System with Unilateral Constraints

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Communications in Theoretical Physics 2008年第3期49卷 575-578页

作者： JING Hong-Xing li yuan-cheng College of Physics Science and Technology China University of Petroleum （East China） Dongying 257061 China

In this paper, we study the Mei symmetry which can result in a Lutzky conserved quantity for nonholonomic mechanical system with unilateral constraints. The definition and the criterion of the Mei symmetry for the system are given. The necessary and sufficient condition under which the Mei symmetry is a lie symmetry for the system is obtained. A Lutzky conserved quantity deduced from the Mei symmetry is gotten. An example is given to illustrate the application of our results.

关键词： nonholonomic mechanical system unilateral constraint Mei symmetry Lutzky conserved quantity

lie Symmetry and Generalized Mei Conserved Quantity for Nonconservative Dynamical System

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Communications in Theoretical Physics 2008年第5期49卷 1148-1150页

作者： JING Hong-Xing li yuan-cheng College of Physical Science and Technology China University of Petroleum （East China） Dongying 257061 China

Based on the total time derivative along the trajectory of the system, for noneonservative dynamical system, the generalized Mei conserved quantity indirectly deduced from the lie symmetry of the system is studied. Firstly, the lie symmetry of the system is given. Then, the necessary and sumeient condition under which the lie symmetry is a Mei symmetry is presented and the generalized Mei conserved quantity indirectly deduced from the lie symmetry of the system is obtained. Lastly, an example is given to illustrate the application of the result.

关键词： lie symmetry Mei symmetry generalized Mei conserved quantity nonconservative dynamicalsystem

Mei Symmetries and lie Symmetries for Nonholonomic Controllable Mechanical Systems with Relativistic Rotational Variable Mass

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Communications in Theoretical Physics 2009年第6期51卷 1073-1077页

作者： XIA li-li li yuan-cheng WANG Xian-Jun Department of Physics Henan Institute of Education Zhengzhou 450014 China College of Physics Science and Technology China University of Petroleum Dongying 257061 China

The Mei symmetries and the lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the lie symmetries of the system are studied respectively. The necessary and sufficient condition under which the Mei symmetry is lie symmetry is given. The condition under which the Mei symmetries can be led to a new kind of conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the results.

关键词： relativity rotation nonholonomic controllable mechanical system variable mass conserved quantity

lie-Form Invariance of a Type of Non-holonomic Singular Systems

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Communications in Theoretical Physics 2007年第3期47卷 409-412页

作者： WANG Jing li yuan-cheng HOU Qi-Bao XIA li-li College of Physical Science and Technology China University of Petroleum Dongying 257061 China

In this paper, the lie-form invariance of a type of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterions of the lie-form invariance for the systems are presented. The Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results.

关键词： non-holonomic constraint singular system symmetry conserved quantity

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

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

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

Unified Symmetry of Nonholonomic Mechanical Systems of Non-Chetaev＇s Type with Unilateral Constraints

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Communications in Theoretical Physics 2006年第6X期46卷 1081-1084页

作者： XIA li-li li yuan-cheng WANG Jing HOU Qi-Bao College of Physical Science and Technology China University of Petroleum Dongying 257061 China

The definition and the criterion for a unified symmetry of nonholonomic mechanical systems of non- Chetaev＇s type with unilateral constraints are presented based on the total time derivative along the trajectory of the system. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced froth the unified symmetry, is obtained. An example is given to illustrate the application of the results.

关键词： unilateral constraints nonholonomic mechanical system of non-Chetaev's type unified symmetry conserved quantity