Conformal invariance and conserved quantities of Appell systems under second-class Mei symmetry

In this paper we introduce the new concept of the conformal invariance and the conserved quantities for Appell systems under second-class Mei symmetry. The one-parameter infinitesimal transformation group and infinitesimal transformation vector of generator are described in detail. The conformal factor in the determining equations under second-class Mei symmetry is found. The relationship between Appell system＇s conformal invariance and Mei symmetry are discussed. And Appell system＇s conformal invariance under second-class Mei symmetry may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result.

Conformal invariance and conserved quantities of Birkhoff systems under second-class Mei symmetry

This paper proposes a new concept of the conformal invariance and the conserved quantities for Birkhoff systems under second-class Mei symmetry. The definition about conformal invariance of Birkhoff systems under second-class Mei symmetry is given. The conformal factor in the determining equations is found. The relationship between Birkhoff system＇s conformal invariance and second-class Mei symmetry are discussed. The necessary and sufficient conditions of conformal invaxiance, which are simultaneously of second-class symmetry, are given. And Birkhoff system＇s conformal invariance may lead to corresponding Mei conserved quantities, which is deduced directly from the second-class Mei symmetry when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result.

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 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.

A conformal invariance for generalized Birkhoff equations

In this article, generalized Birkhoff equations are put forward by adding supplementary terms to the Birkhoff equations. A conformal invariance of the Birkhoff equations can be used to study the generalized Birkhoff Equations, and two examples are presented to illustrate the application of the results.

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 controllablemechanical systems are reported.Criterion and restriction equations determining Mei symmetry after beingdisturbed of the system are established.Form and existence condition of Mei adiabatic invariants are obtained.

Perturbation and Adiabatic Invariants of Mei Symmetry for Nonholonomic Mechanical Systems

基于这个概念断热不变，不安和为 nonholonomic 的 Mei 对称的断热的 invariants 机械系统被学习。为没有不安的系统的 Mei 对称的准确 invariants 被给。到 Meisymmetry 的不安被讨论，为使不安的系统的 Mei 对称的断热的 invariants 被获得。

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

基于这个概念断热不变，不安到 Noether Mei 对称和为 nonholonomic 的断热的 invariants 在阶段空间的机械系统被学习。到为系统的 Noether Mei 对称的不安的定义被介绍，并且到 Noether Mei 对称的不安的标准被给。同时， Noether 断热的 invariants 和 Mei 为使不安的系统的断热的 invariants 被获得。

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 Meiadiabatic 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 invariantsfor 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 andthe Mei adiabatic invariants for the perturbed system are obtained.

Perturbation to Mei Symmetry and Noether Adiabatic Invariants for Birkhoffian Systems

基于这个概念断热不变，不安到 Mei 对称和 Noether 为 Birkhoffian 系统的断热的 invariants 被学习。为没有不安的系统的 Mei 对称的准确 invariants 被给。到 Mei 对称的不安被讨论，从不安导致到系统的 Mei 对称的 Noether 断热的 invariants 被获得。

Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space

This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.

Conformal Invariance and Noether Symmetry, Lie Symmetry of Birkhoffian Systems in Event Space

这份报纸集中于学习保角的不变性和 Noether 对称，为在事件空格的一个 Birkhoffian 系统的谎言对称。系统的保角的不变性的定义被给。由在保角的不变性和 Noether 对称之间的关系上的调查，保角的不变性和谎言对称，在这些情形下面的系统的保角的因素的表情被获得。Noether 保存了数量，保存数量直接从保角的不变性导出的 Hojman 被给。二个例子被给说明结果的申请。

机电系统Mei对称性的共形不变性与守恒量

研究机电系统Mei对称性的共性不变性与守恒量.由系统的Lagrange-Maxwell方程,给出系统Mei对称性的共性不变性,导出系统Mei对称性的共性不变性的相关条件,得到系统的确定方程,讨论共形不变性与Noether对称性,Lie对称性以及Mei对称性之间的关系及相应的守恒量.举例说明结果的应用.

相空间中离散完整系统Mei对称性摄动与绝热不变量

研究相空间中离散完整系统Mei对称性摄动和绝热不变量。给出未受扰动系统Mei对称性导致的精确不变量,讨论在小扰动作用下系统Mei对称性的摄动,得到系统的Mei对称性摄动导致的绝热不变量。最后举例说明结果的应用。

完整系统Tzénoff方程Mei对称性的共形不变性与守恒量

研究了完整力学系统Tzénoff方程Mei对称性的共形不变性及其守恒量,首先建立了完整系统的Tzénoff方程,给出了完整系统Tzénoff方程的Mei对称性及其共形不变性的确定方程,得到了这种共形不变性产生守恒量的条件和导出守恒量的函数式,最后给出一个应用实例.

约束Hamilton系统Mei对称性的摄动和绝热不变量

基于一般力学系统的对称性与守恒量理论,研究了相空间中奇异系统Mei对称性的摄动与绝热不变量问题.首先,给出了约束Hamilton系统的正则方程、系统Mei对称性确定方程、限制方程、附加限制方程以及结构方程和精确不变量的存在形式,在此基础上研究了系统正则方程受微扰后,系统无限小生成元的变化,得到了系统Mei对称性摄动确定方程以及导致的Mei绝热不变量的形式和条件;其次,讨论了系统Mei对称性摄动与Noether对称性摄动、Lie对称性摄动之间的关系,并寻求了其他形式的高阶绝热不变量;最后,通过实例验证了本文结果的正确性.

离散完整力学系统的Mei对称性共形不变性

基于离散完整系统的差分Euler-Lagrange方程,研究离散完整力学系统的Mei对称性共形不变性和守恒量.提出了该系统Mei对称性共形不变性的定义和确定方程.结合规范函数和共形因子,得到在无限小单参数点变换群作用下系统的共形不变性导致的守恒量形式.举例说明结果的应用.

梯度系统的共形不变性与Mei守恒量

考虑梯度系统在无限小变换下的Mei对称性与共形不变性.给出梯度系统Mei对称性的定义和确定方程及其导致的Mei守恒量,并给出梯度系统的共形不变性同时是Mei对称性的充分必要条件,得到了梯度系统共形不变性通过Mei对称性导致的Mei守恒量.

基于非标准Lagrange函数动力学系统的Mei对称性摄动与绝热不变量

研究非标准Lagrange函数下动力学系统的Mei对称性摄动与绝热不变量.首先,给出系统的Euler-Lagrange方程与Mei对称性判据方程及精确不变量;其次,给出受小扰动后系统的运动微分方程,并研究该系统受小扰动作用下Mei对称性摄动与绝热不变量,得到了受扰动后系统的Mei型绝热不变量;最后,举例说明结果的应用.