Symmetry and conserved quantities of discrete generalized Birkhoffian system

The Noether symmetry,the Mei symmetry and the conserved quantities of discrete generalized Birkhoffian system are studied in this paper.Using the difference discrete variational approach,the difference discrete variational principle of discrete generalized Birkhoffian system is derived.The discrete equations of motion of the system are established.The criterion of Noether symmetry and Mei symmetry of the system is given.The discrete Noether and Mei conserved quantities and the conditions for their existence are obtained.Finally,an example is given to show the applications of the results.     

离散变质量完整系统的Noether对称性与Mei对称性

本文研究离散变质量完整系统的Noether对称性与Mei对称性.首先用差分离散变分的方法,建立起离散变质量完整系统的运动方程和能量演化方程.然后给出该系统的Noether对称性和Mei对称性的定义及离散Noether守恒量的形式.得到系统的Noether对称性与Mei对称性导致离散Noether守恒量的条件.最后举例说明结果的应用.     

A Unified Symmetry of Mechanical Systems with Variable Mass in Phase Space

In this paper, the definition and the criterion of a unified symmetry of the mechanical system with variable mass in phase space are given. The Noether conserved quantity, the generalized Hojman conserved quantity, and Mei conserved quantity deduced from the unified symmetry are obtained. An example is given to illustrate the application of the results.     

A Unified Symmetry of Mechanical Systems with Variable Mass in Phase Space

In this paper, the definition and the criterion of a unified symmetry of the mechanical system with variable mass in phase space are given. The Noether conserved quantity, the generalized Hojman conserved quantity, and Mei conserved quantity deduced from the unified symmetry are obtained. An example is given to illustrate the application of the results.     

Mei Symmetry and Lie Symmetry of the Rotational Relativistic Variable Mass System

The Mei symmetry and the Lie symmetry of a rotational relativistic variable mass system are studied. The definitions and criteria of the Mei symmetry and the Lie symmetry of the rotational relativistic variable mass system are given. The relation between the Mei symmetry and the Lie symmetry is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.     

Mei Symmetry and Lie Symmetry of the Rotational Relativistic Variable Mass System

The Mei symmetry and the Lie symmetry of a rotational relativistic variable masssystem are studied. Thedefinitions and criteria of the Mei symmetry and the Lie symmetry of the rotational relativistic variable mass system aregiven. The relation between the Mei symmetry and the Lie symmetry is found. The conserved quantities which the Meisymmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.     

Unified Symmetry and Conserved Quantities of Mechanical System in Phase Space

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.     

Two New Types of Conserved Quantities Deduced from Noether Symmetry for Nonholonomic Mechanical System

For a nonholonomic mechanical system, the generalized Mei conserved quantity and the new generalized Hojman conserved quantity deduced from Noether symmetry of the system are studied. The criterion equation of the Noether symmetry for the system is got. The conditions under which the Noether symmetry can lead to the two new conserved quantities are presented and the forms of the conserved quantities are obtained. Finally, an example is given to illustrate the application of the results.     

Emden方程的Mei对称性、Lie对称性和Noether对称性

研究Emden动力学方程的形式不变性即Mei对称性，给出其定义和确定方程，研究Emden方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量，给出一个例子说明结果的应用. 关键词： Emden动力学方程 Mei对称性 Noether对称性 Lie对称性     

Noether-Mei Symmetry of Mechanical System in Phase Space

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 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.     

Hamilton系统的Mei对称性、Noether对称性和Lie对称性

研究Hamilton系统的形式不变性即Mei对称性，给出其定义和确定方程.研究Hamilton系统的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量.给出一个例子说明本文结果的应用. 关键词： Hamilton系统 Mei对称性 Noether对称性 Lie对称性 守恒量     

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.     

一类完整系统的Mei对称性与守恒量

对一类完整系统的方程给出其Mei对称性的定义和判据.如果Mei对称性是Noether对称性,则可找到Noether守恒量.如果Mei对称性是Lie对称性,则可找到Hojman型守恒量.举例说明结果的应用. 关键词： 分析力学 完整系统 Mei对称性 守恒量     

Mei Symmetry and Lie Symmetry of Relativistic Hamiltonian System

The Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are studied. The definition and criterion of the Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are given. The relationship between them is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained.An example is given to illustrate the application of the result.     

相空间中离散完整系统的Noether对称性和Mei对称性

研究相空间中离散完整系统的Noether对称性、Mei对称性及其导致的守恒量.利用差分离散变分方法,给出相空间中离散完整系统的差分离散变分原理,建立系统的离散正则方程和能量演化方程;给出系统Noether对称性和Mei对称性的判定条件,得到系统离散形式的Noether守恒量和Mei守恒量及其存在的条件.举例说明结果的应用. 关键词： 相空间 离散完整系统 对称性 守恒量     

Vacco动力学方程的Mei对称性、Lie对称性和Noether对称性

研究Vacco动力学方程的形式不变性即Mei对称性，给出其定义和确定方程，研究Vacco动力学方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量，给出一 个例子说明结果的应用. 关键词： Vacco动力学方程 Mei对称性 Noether对称性 Lie对称性 守恒量     

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

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.     

Mei Symmetry and Lie Symmetry of Relativistic Hamiltonian System

The Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are studied. The definition and criterion of the Mei symmetry and the Lie symmetry of the reoativistic Hamiltonian system are given. The relationship between them is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.     

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.