具有单面完整约束的有多余坐标力学系统的Lie对称性与守恒量

研究具有单面完整约束的有多余坐标力学系统的Lie对称性与守恒量.利用常微分方程在无限小变换下的不变性,建立了系统Lie对称性的确定方程、限制方程和附加限制方程,得到了结构方程与守恒量的形式;并研究了上述问题的逆问题,即根据系统的已知积分来求相应的Lie对称性.文末举例说明结果的应用.     

方程的形式不变性

研究完整系统Routh方程的形式不变性.给出在无限小变换下Routh方程的形式不变性的定义和判据,讨论了形式不变性与Noether对称性以及Lie对称性的关系.     

方程的形式不变性(英文)

研究完整系统Routh方程的形式不变性 .给出在无限小变换下Routh方程的形式不变性的定义和判据 ,讨论了形式不变性与Noether对称性以及Lie对称性的关系     

Chetaev型非完整约束系统的Lie对称性逆问题

研究非完整系统的Ｌｉｅ对称性逆问题：根据已知识分求相应的Ｌｉｅ对称性。首先，由已知识分求出相应的Ｎｏｅｔｈｅｒ对称性；其次，由Ｎｏｅｔｈｅｒ对称性通过验证确定方程和限制方程来求得Ｌｉｅ对称性。具体研究了受Ｃｈｅｔａｅｖ型非完整约束系统的Ｌｉｅ对称性逆问题。     

单面非完整系统相对运动动力学的Lie对称性

在相空间中研究具有单面非完整约束系统相对于非惯性系的Lie对称性与守恒量。首先，给出了系统的运动微分方程；其次，根据微分方程在无限小变换下的不变性建立Lie对称性的确定方程和限制方程，给出结构方程和守恒量；最后，讨论了系统的Lie对称性逆问题，并举例说明结果的应用。     

具有单面完整约束的有多余坐标力学系统的Lie对称性与？…

研究具有单面完整约束的有多余坐标力学系统的Ｌｉｅ对称性与守恒量。利用常微分方程在无限小变换下的汪变性，建立了系统Ｌｉｅ对称性的确定方程、限制方程和附加限制方程，得到了结构方程与守恒坦的形式，并研究了上术问题的逆问题，即根据系统的已知积分来求相应的Ｌｉｅ对称性。文末举例说明结果的应用。     

单面完整系统相对于非惯性系的Lie对称性与守恒量

研究单元完整系统相对于非惯性系的 Lie对称性与守恒量。首先利用微分方程在无限小变换下的不变性建立系统 Lie对称所满足的确定方程和限制方程 ,给出了结构方程和守恒量 ;其次研究系统 Lie对称逆问题 ;最后举例说明结果的应用     

关于Kepler方程的对称性

对平面Kepler方程在群的无限小变换下的Noether对称性、Lie对称性及其导出的守恒量进行了研究,给出了2种对称性之间的关系.     

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.     

任意阶非完整系统的Lie对称性与守恒量

利用常微分方程在无限小变换下的不变性研究带任意阶非完整约束的力学系统的Lie对称性与守恒量 .得到确定方程、限制方程、结构方程以及守恒量的形式 .     

Lie Symmetry and Hojman Conserved Quantity of Maggi Equations

Lie symmetry of Maggi equations is studied. Its determining equation and restriction equation of nonholonomic constraint are given. A Hojman conserved quantity can be deduced directly by using the Lie symmetry. An example is given to illustrate the application of the result.     

Weak Noether symmetry and conserved laws of Birkhoffian systems

A new kind of weak Noether symmetry is obtained that arises in the study of Birkhoffian systems.The conserved quantities,which includes Noether conserved quantity,Hojman type conserved quantity and new type conserved quantity,are also calculated from this symmetry.Finally,two examples are presented to illustrated the application of these new results.     

Lie symmetries and conserved quantities for generalized Birkhoff system

To study Lie symmetry and the conserved quantity of a generalized Birkhoff system with additional terms,the determining equations of the Lie symmetry of the system is derived.A conserved quantity of Hojman’s type and a Noether’s conserved quantity are deduced by the Lie symmetry under some conditions.One example is given to illustrate the application of the result.     

Perturbation to Noether Quasi-Symmetry and Adiabatic Invariants for Nonholonomic Systems on Time Scales

Perturbation to Noether quasi-symmetry and adiabatic invariants for the nonholonomic system on time scales are studied. Firstly, some properties of time scale calculus are reviewed. Secondly, the differential equations of motion for the nonholonomic system on time scales, Noether quasi-symmetry and conserved quantity are given. Thirdly, perturbation to Noether quasi-symmetry and adiabatic invariants, which are the main results of this paper, are investigated. The main results are achieved by two steps, the first step is to obtain adiabatic invariants without transforming the time, and the next is to obtain adiabatic invariants under the infinitesimal transformations of both the time and the coordinates. And in the end, an example is given to illustrate the methods and results.