Perturbation to Mei symmetry and Mei adiabatic invariants for discrete generalized Birkhoffian system

Based on the concept of discrete adiabatic invariant,this paper studies the perturbation to Mei symmetry and Mei adiabatic invariants of the discrete generalized Birkhoffian system.The discrete Mei exact invariant induced from the Mei symmetry of the system without perturbation is given.The criterion of the perturbation to Mei symmetry is established and the discrete Mei adiabatic invariant induced from the perturbation to Mei symmetry is obtained.Meanwhile,an example is discussed to illustrate the application of the results.     

Perturbation to Mei symmetry and adiabatic invariants for Hamilton systems

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

非完整力学系统Mei对称性的摄动及其导致的一类新型Mei绝热不变量

研究非完整力学系统Mei对称性的摄动及其导致的新型Mei绝热不变量. 给出了系统Mei对称性的判据方程和结构方程在受微扰后变化的形式, 得到了系统Mei对称性的摄动导致的新型Mei绝热不变量的形式和条件. 关键词： 非完整力学系统 Mei对称性 摄动 Mei绝热不变量     

Perturbation and Adiabatic Invariants of Mei Symmetry for Nonholonomic Mechanical Systems

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.     

Perturbation to Mei Symmetry and Adiabatic Invariants for Nonholonomic Systems in Terms of Quasi-Coordinates

Based on the concept of adiabatic invariant, the perturbation to Meisymmetry and adiabatic invariants for nonholonomic mechanical systems interms of quasi-coordinates are studied. The definition of the perturbationto Mei symmetry for the system is presented, and the criterion of theperturbation to Mei symmetry is given. Meanwhile, the Mei adiabaticinvariants for the perturbed system are obtained.     

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

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

Perturbation to Mei Symmetry and Generalized Mei Adiabatic Invariants for Nonholonomic Systems in Terms of Quasi-Coordinates

By introducing the coordination function f, the generalized Mei conserved quantities for the nonholonomic systems in terms of quasi-coordinates are given. Then based on the concept of adiabatic invariant, the perturbation to Mei symmetry and the generalized Mei adiabatic invariants for nonholonomic systems in terms of quasi-coordinates are studied.     

Perturbation to Mei Symmetry and Generalized Mei Adiabatic Invariants for Birkhoffian Systems

This paper investigates the perturbation to Mei symmetry for Birkhoffian systems. The criterion equation of the perturbation to Mei symmetry is established. The condition for existence of generalized Mei adiabatic invariant induced directly from the perturbation to Mei symmetry is obtained, and its form is presented. Finally, an example is discussed to further illustrate the application of the results.     

Perturbation to Mei Symmetry and Adiabatic Invariants for Disturbed El-Nabulsi's Fractional Birkhoff System

For El-Nabulsi's fractional Birkhoff system, Mei symmetry perturbation, the corresponding Mei-type adiabatic invariants and Noether-type adiabatic invariants are investigated in this paper. Firstly, based on El-Nabulsi-Birkhoff fractional equations, Mei symmetry and the corresponding Mei conserved quantity, Noether conserved quantity deduced indirectly by Mei symmetry are studied. Secondly, Mei-type exact invariants and Noether-type exact invariants are given on the basis of the definition of adiabatic invatiant. Thirdly, Mei symmetry perturbation, Mei-type adiabatic invariants and Noether-type adiabatic invariants for the disturbed El-Nabulsi's fractional Birkhoff system are studied. Finally, two examples, Hojman-Urrutia problem for Mei-type adiabatic invariants and another for the Noether-type adiabatic invariants, are given to illustrate the application of the results.     

Perturbation to Mei Symmetry and Adiabatic Invariants for Disturbed El-Nabulsi's Fractional Birkhoff System

For El-Nabulsi's fractional Birkhoff system, Mei symmetry perturbation, the corresponding Mei-type adiabatic invariants and Noether-type adiabatic invariants are investigated in this paper. Firstly, based on El-NabulsiBirkhoff fractional equations, Mei symmetry and the corresponding Mei conserved quantity, Noether conserved quantity deduced indirectly by Mei symmetry are studied. Secondly, Mei-type exact invariants and Noether-type exact invariants are given on the basis of the definition of adiabatic invatiant. Thirdly, Mei symmetry perturbation, Mei-type adiabatic invariants and Noether-type adiabatic invariants for the disturbed El-Nabulsi's fractional Birkhoff system are studied.Finally, two examples, Hojman-Urrutia problem for Mei-type adiabatic invariants and another for the Noether-type adiabatic invariants, are given to illustrate the application of the results.     

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

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

Perturbation to Lie-Mei Symmetry and Adiabatic Invariants for Birkhoffian Systems

Based on the concept of adiabatic invariant, the perturbation to Lie-Mei symmetry and adiabatic invariants for Birkhoffian systems are studied. The definition of the perturbation to Lie-Mei symmetry for the system is presented, and the criterion of the perturbation to Lie-Mei symmetry is given. Meanwhile, the Hojman adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained.     

Perturbation to Noether-Mei Symmetry and Adiabatic Invariants for Nonholonomic Mechanical Systems in Phase Space

Based on the concept of adiabatic invariant, the perturbation to Noether Mei symmetry and adiabatic invariants for nonholonomie mechanical systems in phase space are studied. The definition of the perturbation to Noether-Mei symmetry for the system is presented, and the criterion of the perturbation to Noether-Mei symmetry is given. Meanwhile, the Noether adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained.     

Mei Adiabatic Invariants Induced by Perturbation of Mei Symmetry forNonholonomic Controllable Mechanical Systems

Two types of Mei adiabatic invariants induced by perturbation of Mei symmetry for nonholonomic controllable mechanical systems are reported. Criterion and restriction equations determining Mei symmetry after being disturbed of the system are established. Form and existence condition of Mei adiabatic invariants are obtained.     

Perturbation to Unified Symmetry and Adiabatic Invariants for Relativistic Hamilton Systems

Based on the concept of adiabatic invariant, the perturbation to unified symmetry and adiabatic invariants for relativistic Hamilton systems are studied. The definition of the perturbation to unified symmetry for the system is presented, and the criterion of the perturbation to unified symmetry is given. Meanwhile, the Noether adiabatic invariants, the generalized Hojman adiabatic invariants, and the Mei adiabatic invariants for the perturbed system are obtained.     

Mei Adiabatic Invariants Induced by Perturbation of Mei Symmetry for Nonholonomic Controllable Mechanical Systems

Two types of Mei adiabatic invariants induced by perturbation of Mei symmetry for nonholonomic controllable mechanical systems are reported. Criterion and restriction equations determining Mei symmetry after being disturbed of the system are established. Form and existence condition of Mei adiabatic invariants are obtained.     

非保守动力学系统Noether对称性的摄动与绝热不变量

基于非保守系统的El-Nabulsi动力学模型, 研究了非保守动力学系统Noether对称性的摄动与绝热不变量问题.首先, 引入El-Nabulsi在分数阶微积分框架下基于Riemann-Liouville分数阶积分提出的类分数阶变分问题, 列出非保守系统的Euler-Lagrange方程; 其次, 给出了Noether准对称变换的定义和判据, 建立了Noether对称性与不变量之间的关系, 得到了精确不变量; 最后, 提出并研究了该系统受小扰动作用后Noether对称性的摄动与绝热不变量问题, 证明了绝热不变量存在的条件及形式, 并举例证明结果的应用. 关键词： 非保守系统 El-Nabulsi动力学模型 对称性摄动 绝热不变量     

Perturbation to Lie-Mei Symmetry and Adiabatic Invariants for Birkhoffian Systems

Based on the concept of adiabatic invariant, the perturbation to Lie-Mei symmetry and adiabatic invariants for Birkhoffian systems are studied. The definition of the perturbation to Lie-Mei symmetry for the system is presented, and the criterion of the perturbation to Lie-Mei symmetry is given. Meanwhile, the Hojman adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained.     

Mei Symmetry of General Discrete Holonomic System

The Mei symmetry and conserved quantity of general discrete holonomic system are investigated in this paper. The requirement for an invariant formalism of discrete motion equations is defined to be Mei symmetry. The criterion when a conserved quantity may be obtained from Mei symmetry is also deduced. An example is discussed for applications of the results.     

Perturbation to Lie Symmetry and Lutzky Adiabatic Invariants for Lagrange Systems

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.