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.     

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 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 Mei adiabatic invariants for mechanical systems in phase space

For a perturbed mechanical system in phase space, considering d/dt in the structure equation and process of proof including infinitesimal parameter ε obviously, this paper studies the perturbation to Mei symmetry and adiabatic invariants. Firstly, the exact invariant induced directly from the Mei symmetry of the system without perturbation is given. Secondly, based on the concept of high-order adiabatic invariant, the determining equations of the perturbation to Mei symmetry are established, the condition of existence of the Mei adiabatic invariant led by the perturbation to Mei symmetry is obtained, and its form is presented. Lastly, an example is given to illustrate the application of the results.     

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.     

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.     

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     

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.     

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.     

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.     

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.     

广义Hamilton系统的Mei对称性导致的Mei守恒量

研究广义Hamilton系统的Mei对称性导致的守恒量. 首先,在群的一般无限小变换下给出广义Hamilton系统的Mei对称性的定义、判据和确定方程;其次,研究系统的Mei守恒量存在的条件和形式,得到Mei对称性直接导致的Mei守恒量; 而后,进一步给出带附加项的广义Hamilton系统Mei守恒量的存在定理; 最后,研究一类新的三维广义Hamilton系统,并研究三体问题中3个涡旋的平面运动. 关键词： 广义Hamilton系统 Mei对称性 Mei守恒量 三体问题     

非完整系统Nielsen方程的Mei对称性与Mei守恒量

研究了Chetaev型非完整非保守系统带乘子的Nielsen方程的Mei对称性和Mei守恒量-对Chetaev型非完整非保守系统带乘子的Nielsen方程的运动微分方程、Mei对称性的定义和判据、Mei对称性直接导致的Mei守恒量的条件以及守恒量的形式进行了具体的研究-举例说明结果的应用- 关键词： 非完整系统 Nielsen方程 Mei对称性 Mei守恒量     

Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style

This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.     

Perturbation of Symmetries and Mei Adiabatic Invariants of Nonholonomic Systems with Servoconstraints

The perturbation of symmetries and Mei adiabatic invariants of nonholonomic systems with servoconstraints are studied. The exact invariants in the form of Mei conserved quantities introduced by the Mei symmetry of nonholonomic systems with servoconstraints without perturbations are given. Based on the definition of higher-order adiabatic invariants of mechanical systems, the perturbation of Mei symmetries for nonholonomic .systems with servoconstraints under the action of small disturbance is investigated, and Mei adiabatic invatiants of the system are obtained. An example is given to illustrate the application of the results.     

相对运动动力学系统Appell方程Mei对称性导致的Mei守恒量

研究相对运动动力学系统Appell方程的Mei对称性及其直接导致的Mei守恒量.在群的无限小变换下,给出相对运动动力学系统Appell方程Mei对称性的定义和判据;得到相对运动动力学系统Appell方程Mei对称性的结构方程以及Mei对称性直接导致的Mei守恒量的表达式.举例说明结果的应用. 关键词： 相对运动动力学 Appell方程 Mei对称性 Mei守恒量     

Structure equation and Mei conserved quantity for Mei symmetry of Appell equation

This paper investigates structure equation and Mei conserved quantity of Mei symmetry of Appell equations for non-Chetaev nonholonomic systems. Appell equations and differential equations of motion for non-Chetaev nonholonomic mechanical systems are established. A new expression of the total derivative of the function with respect to time $t$ along the trajectory of a curve of the system is obtained, the definition and the criterion of Mei symmetry of Appell equations under the infinitesimal transformations of groups are also given. The expressions of the structure equation and the Mei conserved quantity of Mei symmetry in the Appell function are obtained. An example is given to illustrate the application of the results.     

事件空间中非Chetaev型非完整系统的Mei对称性与Mei守恒量

研究了事件空间中非Chetaev型非完整系统的Mei对称性和Mei守恒量.给出了事件空间中非Chetaev型非完整系统的运动微分方程、Mei对称性的定义和判据、Mei对称性直接导致的Mei守恒量的条件以及Mei守恒量的形式.并举例说明了结论的应用.     

Mei symmetry and Mei conserved quantity of Nielsen equations for a non-holonomic system of Chetaev’s type with variable mass

Mei symmetry and Mei conserved quantity of Nielsen equations for a non-holonomic, non-conservative system of Chetaev's type with variable mass are studied. The differential equations of motion of the Nielsen equation for the system, the definition and criterion of Mei symmetry, and the condition and the form of Mei conserved quantity deduced directly by Mei symmetry for the system are obtained. An example is given to illustrate the application of the results.