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Perturbation and Adiabatic Invariants of Mei Symmetry for Nonholonomic Mechanical Systems

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Communications in Theoretical Physics 2007年第4期47卷 594-596页

作者： ding ning fang jian-hui WANG Peng College of Physical Science and Technology China University of Petroleum Dongying 257061 China

Based on the concept of adiabatic invariant, the perturbation and adiabatic invariants of the Mei symmetry for nonholonomic mechanical systems are studied. The exact invariants of the Mei symmetry for the system without perturbation are given. The perturbation to the Mei symmetry is discussed and the adiabatic invariants of the Mei symmetry for the perturbed system are obtained.

关键词： Mei symmetry perturbation adiabatic invariant nonholonomic mechanical system

A New Type of Conserved Quantity of Mei Symmetry for Lagrange Systems

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Communications in Theoretical Physics 2007年第5X期48卷 799-800页

作者： ding ning fang jian-hui WANG Peng ZHANG Xiao-Ni College of Physics Science and Technology China University of Petroleum Dongying 257061 China

A new type of conserved quantity, which is induced from the Mei symmetry of Lagrange systems, is studied. The conditions for that the new type of conserved quantity exists and the form of the new type of conserved quantity are obtained. An illustrated example is given. The Noether conserved quantity induced from the Mei symmetry of Lagrange systems is a special case of the new type of conserved quantity given in this paper.

关键词： Mei symmetry new type of conserved quantity Lagrange system

Perturbation to Lie Symmetry and Lutzky Adiabatic Invariants for Lagrange Systems

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Communications in Theoretical Physics 2008年第1期49卷 57-60页

作者： ding ning fang jian-hui WANG Peng ZHANG Xiao-Ni College of Physics Science and Technology China University of Petroleum Dongying 2570617 China

Based on the concept of adiabatic invariant, perturbation to Lie symmetry and Lutzky adiabatic invariants for Lagrange systems are studied by using different methods from those of previous works. Exact invariants induced from Lie symmetry of the system without perturbation are given. Perturbation to Lie symmetry is discussed and Lutzky adiabatic invariants of the system subject to perturbation are obtained.

关键词： symmetry perturbation Lutzky adiabatic invariant Lagrange system

Perturbation to Lie Symmetry and Adiabatic Invariants for General Holonomic Mechanical Systems

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Communications in Theoretical Physics 2007年第7期48卷 19-22页

作者： ding ning fang jian-hui WANG Peng ZHANG Xiao-Ni College of Physics Science and Technology,China University of Petroleum,Dongying 257061,China College of Physics Science and Technology China University of Petroleum

Based on the concept of adiabatic invariant,the perturbation to the Lie symmetry and adiabatic invariantsfor general holonomic mechanical systems are *** exact invariants induced directly from the Lie symmetryof the system without perturbation are *** perturbation to the Lie symmetry is discussed and the adiabaticinvariants that have the different form from that in[***.55(2006)3236(in Chinese)]of the perturbedsystem,are obtained.

关键词： Lie symmetry perturbation adiabatic invariant general holonomic mechanical’system

Perturbation to Mei Symmetry and Noether Adiabatic Invariants for Birkhoffian Systems

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Communications in Theoretical Physics 2008年第6期49卷 1410-1412页

作者： ding ning fang jian-hui Department of Physics and Electronics Science Binzhou University Binzhou 256600 China College of Physics Science and Technology China University of Petroleum Dongying 257061 China

Based on the concept of adiabatic invariant, the perturbation to Mei symmetry and Noether adiabatic invariants for Birkhoffian systems are studied. The exact invariants of Mei symmetry for the system without perturbation are given. The perturbation to Mei symmetry is discussed and the Noether adiabatic invariants induced from the perturbation to Mei symmetry of the system are obtained.

关键词： Mei symmetry perturbation Noether adiabatic invariant Birkhoffian system

A New Type of Mei Adiabatic Invariant Induced by Perturbation to Mei Symmetry of Hamiltonian Systems

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Communications in Theoretical Physics 2009年第7期52卷 12-16页

Considering full perturbation to infinitesimal generators in the Mei structure equation,a new type of Meiadiabatic invariant induced by perturbation to Mei symmetry for Hamiltonian system was reported.

关键词： Mei symmetry perturbation Mei adiabatic invariant Hamiltonian system

Noether-Mei Symmetry of Mechanical System in Phase Space

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Communications in Theoretical Physics 2006年第5期45卷 882-884页

作者： fang jian-hui WANG Peng ding ning College of Physical Science and Technology China University of Petroleum Dongying 257061 China

In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i,e., a Noether-Mei symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the Mei conserved quantity deduced from the Noether-Mei symmetry of the system are obtained. Finally, two examples are given to illustrate the Bpplication of the results.

关键词： Noether-Mei symmetry conserved quantity mechanical system phase space

Two New Types of Conserved Quantities of Mei Symmetry for Holonomic Mechanical System

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Communications in Theoretical Physics 2008年第1期49卷 53-56页

作者： fang jian-hui WANG Peng ding ning College of Physics Science and Technology China University of Petroleum Dongying 257061 China

Two new types of conserved quantities directly deduced by Mei symmetry of holonomic mechanical system are studied. The definition and criterion of Mei symmetry for holonomic system are given. A coordination function is introduced, the conditions under which the Mei symmetry can directly lead to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The result indicates that the coordination function can be selected properly according to the demand of the gauge function, thereby the gauge function can be found out more easily. Furthermore, since the choice of the coordination function has multiformity, much T more conserved quantity of Mei symmetry for holonomic mechanical system can be obtained.

关键词： holonomic mechanical system Mei symmetry new conserved quantity

Unified Symmetry and Conserved Quantities of Mechanical System in Phase Space

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Communications in Theoretical Physics 2006年第1X期46卷 97-100页

作者： fang jian-hui ding ning WANG Peng College of Physics Science and Technology China University of Petroleum Dongying 257061 China

In this paper, a new symmetry and its conserved quantities of a mechanical system in phase space are studied. The defition of this new symmetry, i.e., a unified one is presented, and the criterion of this symmetry is also given. The Noether, the generalized Hojman and the Mei conserved quantities of the unified symmetry of the system are obtained. The unified symmetry contains the Noether, the Lie and the Mei symmetries, and has more generalized significance.

关键词： unified symmetry mechanical system conserved quantity phase space