单面完整约束系统在相空间中的形式不变性

对单面完整约束系统在相空间中的形式不变性进行了分析研究。给出了单面完整约束系统在相空间中形式不变性的定义和判据 ,得到了形式不变性的结构方程和守恒量 ,并用实际算例验证了研究结果的有效性。     

Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems

This paper studies conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems. Third-order Lagrange equations, the definition and a determining equation of conformal invariance of the system are presented. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and sufficient condition that conformal invariance of the system would have Lie symmetry under single-parameter infinitesimal transformations is obtained. The corresponding conserved quantity of conformal invariance is derived with the aid of a structure equation. Lastly, an example is given to illustrate the application of the results.     

离散差分序列变质量Hamilton系统的Lie对称性与Noether守恒量

本文研究离散差分序列变质量Hamilton系统的Lie对称性与Noether守恒量. 构建了离散差分序列变质量Hamilton系统的差分动力学方程, 给出了离散差分序列变质量Hamilton系统差分动力学方程在无限小变 换群下的Lie对称性的确定方程和定义, 得到了离散力学系统Lie对称性导致Noether守恒量的条件及形式, 举例说明结果的应用. 关键词： 离散力学 Hamilton系统 Lie对称性 Noether守恒量     

非完整力学系统的Noether-Lie对称性

研究了非完整力学系统的一种新对称性——Noether-Lie对称性及其守恒量. 给出了非完整力学系统Noether -Lie对称性的定义和判据，提出系统的Noether-Lie对称性导致Noether守恒量和广义Hojman守恒量的定理. 举例说明了结果的应用. Hojman守恒量是所给出的广义Hojman守恒量的特例. 关键词： 非完整力学系统 Noether-Lie对称性 Noether守恒量 广义Hojman守恒量     

相空间中变质量力学系统Lie-Mei对称性的两个守恒量

研究相空间中变质量力学系统Lie-Mei对称性导致的两个守恒量,给出系统Lie-Mei对称性的定义和判据,引入谐调函数,得到系统Lie-Mei对称性导致的两个守恒量的条件和形式,并给出应用算例. 由于谐调函数可根据寻找规范函数的需要适当选取,且选取具有多样性,因此能够找到系统Lie-Mei对称性更多的守恒量. 关键词： 相空间 变质量系统 Lie-Mei对称性 守恒量     

Lie symmetry and Mei symmetry of a rotational relativistic system in phase space

The Lie symmetry and the Mei symmetry of a rotational relativistic system in phase space are studied. The definition, criterion and conserved quantity of the Lie symmetry and the Mei symmetry of a rotational relativistic system in phase space are given. The relation between the Lie symmetry and the Mei symmetry is found. An example is given to illustrate the application of the result.     

变质量单面完整约束系统的Mei对称性

研究变质量单面完整约束系统的Mei对称性. 给出变质量单面完整约束系统Mei对 称性的定义和判据,得到Mei对称性的结构方程和守恒量,并举例说明结果的应用. 关键词： 变质量 单面完整约束 Mei对称性 守恒量     

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.     

Lie symmetries and conserved quantities of second-order nonholonomic mechanical system

The Lie symmetries and the conserved quantities of the second-order nonholonomic mechanical system are studied. Firstly, by using the invariance of the differential equation of motion under the infinitesimal transformations, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equation and the conservative quantities of the Lie symmetries are obtained. Secondly , the inverse problems of the Lie symmetries are studied . Finally , an example is given to illustrate the application of the result.