El-Nabulsi动力学模型下Birkhoff系统Noether对称性的摄动与绝热不变量

基于El-Nabulsi动力学模型,研究了小扰动作用下Birkhoff系统Noether对称性的摄动与绝热不变量问题.首先,将El-Nabulsi提出的在分数阶微积分框架下基于Riemann-Liouville分数阶积分的非保守系统动力学模型拓展到Birkhoff系统,建立El-Nabulsi-Birkhoff方程;其次,基于在无限小变换下El-Nabulsi-Pfaff作用量的不变性,给出Noether准对称性的定义和判据,得到了Noether对称性导致的精确不变量;再次,引入力学系统的绝热不变量概念,研究El-Nabulsi动力学模型下受小扰动作用的Birkhoff系统Noether对称性的摄动与绝热不变量之间的关系,得到了对称性摄动导致的绝热不变量的条件及其形式.作为特例,给出了El-Nabulsi动力学模型下相空间中非保守系统和经典Birkhoff系统的Noether对称性的摄动与绝热不变量.以著名的Hojman-Urrutia问题为例,研究其在El-Nabulsi动力学模型下的Noether对称性,得到了相应的精确不变量和绝热不变量.     

El-Nabulsi动力学模型下非Chetaev型非完整系统的精确不变量与绝热不变量

研究El-Nabulsi动力学模型下非Chetaev型非完整系统精确不变量与绝热不变量问题. 首先, 导出El-Nabulsi-d'Alembert-Lagrange原理并建立系统的运动微分方程. 其次, 建立El-Nabulsi模型下未受扰动的非Chetaev 型非完整系统的Noether对称性与Noether对称性导致的精确不变量之间的关系; 再次, 引入力学系统的绝热不变量概念, 研究受小扰动作用下非Chetaev型非完整系统Noether对称性的摄动导致绝热不变量问题, 给出了绝热不变量存在的条件及其形式. 作为特例, 本文讨论了El-Nabulsi模型下Chetaev型非完整系统的精确不变量与绝热不变量问题. 最后分别给出非Chetaev型和Chetaev型两种约束下的算例以说明结果的应用.     

Lagrange系统对称性的摄动与Hojman型绝热不变量

研究Lagrange系统对称性的摄动与绝热不变量.列出未受扰Lagrange系统的Lie对称性导致的Hojman守恒量；基于力学系统的高阶绝热不变量的定义，研究在小扰动作用下Lagrange系统Lie对称性的摄动，得到了系统的一类Hojman形式的绝热不变量.并举例说明结果的应用. 关键词： Lagrange系统 对称性 摄动 绝热不变量     

相空间中非完整可控力学系统的对称性摄动与绝热不变量

研究相空间中非完整可控力学系统的对称性摄动与绝热不变量. 列出相空间中未受扰非完整可控力学系统的形式不变性导致的Noether守恒量. 基于力学系统高阶绝热不变量的定义，研究小扰动作用下相空间中非完整可控力学系统的形式不变性摄动与绝热不变量，给出了精确不变量与绝热不变量存在的条件与形式，并举例说明结果的应用.     

单面约束Birkhoff系统对称性的摄动与绝热不变量

研究了具有单面约束的Birkhoff系统在小扰动作用下对称性的摄动与不变量之间的关系.首先,建立了系统的运动微分方程,给出了系统的精确不变量;其次,基于力学系统的高阶绝热不变量的概念,得到了系统的绝热不变量存在的条件及其形式;最后,举例说明结果的应用 关键词： 分析力学 单面约束 Birkhoff系统 对称性 摄动 绝热不变量     

相空间中离散力学系统对称性的摄动与Hojman型绝热不变量

研究相空间中离散力学系统对称性的摄动与绝热不变量.列出相空间中未受扰离散力学系统的特殊Lie对称性导致的Hojman型精确不变量.基于相空间中力学系统的高阶绝热不变量的定义，研究在小扰动作用下系统Lie对称性的摄动，得到了相空间中离散力学系统的一类新的绝热不变量——Hojman型绝热不变量.举例说明结果的应用. 关键词： 相空间 Lie对称性 摄动 绝热不变量     

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     

广义经典力学系统对称性的摄动与绝热不变量

在高维增广相空间中研究广义经典力学系统的精确不变量和绝热不变量.建立了该空间中系 统的对称性与不变量的关系；基于力学系统受到小干扰力作用的高阶绝热不变量的概念，给出了系统的高阶绝热不变量的形式及存在条件，并建立了绝热不变量与对称变换之间的对应关系；最后，举例说明结果的应用. 关键词： 对称性 摄动 不变量 广义经典力学系统 增广相空间     

事件空间中完整系统的Lie对称性与绝热不变量

研究事件空间中完整力学系统Lie对称性的摄动与绝热不变量.基于力学系统的高阶绝热不变量的概念，研究在小扰动作用下系统Lie对称性的摄动，得到了事件空间中完整力学系统的一类Hojman形式的高阶绝热不变量，给出了绝热不变量存在的条件及形式.并举例说明结果的应用. 关键词： 事件空间 对称性 摄动 绝热不变量     

Birkhoff系统的一类新型绝热不变量

研究Birkhoff系统对称性的摄动与绝热不变量.给出了未受扰Birkhoff系统的Lie对称性导致的Hojman型精确不变量.基于力学系统的高阶绝热不变量的定义，研究在小扰动作用下Birkhoff系统Lie对称性的摄动，得到了系统的一类新型绝热不变量.举例说明结果的应用. 关键词： Birkhoff系统 Lie对称性 摄动 绝热不变量     

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 to symmetries and adiabatic invariants of a type of nonholonomic singular system

Based on the theory of symmetries and conserved quantities, the perturbation to the symmetries and adiabatic invariants of a type of nonholonomic singular system are discussed. Firstly, the concept of higher order adiabatic invariants of the system is proposed. Secondly, the conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Thirdly, we study the inverse problems of the perturbation to symmetries of the system. An example is presented to illustrate these results.     

Perturbation to Mei Symmetry and Noether Adiabatic Invariants for Birkhoffian Systems

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.     

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 Lie symmetry and another type of Hojman adiabatic invariants for Birkhoffian systems

The perturbation to Lie symmetry and another type of Hojman adiabatic invariants induced from the perturbation to Lie symmetry for Birkhoffian systems are studied. The exact invariants of Lie symmetry for the system without perturbation are given. Based on the concept of adiabatic invariant, the perturbation to Lie symmetry is discussed and another new type of Hojman adiabatic invariants that have the different form from that in [Acta Phys. Sin. 55 3833] for the perturbed system are obtained.     

Perturbation to symmetries and Hojman adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints

This paper studies the perturbation to symmetries and adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints. It gives the exact invariants introduced by the Lie symmetries of the nonholonomic controllable mechanical system with non-Chetaev type constraints without perturbation. Based on the definition of high-order adiabatic invariants of mechanical system, the perturbation of Lie symmetries for nonholonomic controllable mechanical system with non-Chetaev type constraints with the action of small disturbances is investigated, and a new type of adiabatic invariant of system are obtained. In the end of this paper, an example is given to illustrate the application of the results.