Conformal invariance and conserved quantity of Hamilton systems

This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration.

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 invaxiance 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.

Conformal invariance,Noether symmetry,Lie symmetry and conserved quantities of Hamilton systems

In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results.

Conformal invariance and Hojman conserved quantities of canonical Hamilton systems

This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invarianee being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.

Non-Noether symmetries of Hamiltonian systems with conformable fractional derivatives

In this paper, we present the fractional Hamilton＇s canonical equations and the fractional non-Noether symmetry of Hamilton systems by the conformable fractional derivative. First/y, the exchanging relationship between isochronous variation and fractional derivatives, and the fractional Hamilton principle of the system under this fractional derivative are proposed. Secondly, the fractional Hamilton＇s canonical equations of Hamilton systems based on the Hamilton principle are established. Thirdly, the fractional non-Noether symmetries, non-Noether theorem and non-Noether conserved quantities for the Hamilton systems with the conformable fractional derivatives are obtained. Finally, an example is given to illustrate the results.

广义经典力学中完整系统Hamilton正则方程的形式不变性

研究广义力学中Hamilton正则方程的形式不变性.给出正则方程形式不变性的定义和判据.建立形式不变性与系统守恒量之间的关系,并举例说明结果的应用.

约束Hamilton系统的共形不变性和守恒量研究

对约束Hamilton系统的共形不变性与新型守恒量进行研究,提出了该系统共形不变性的概念。在无限小变换满足Lie对称性的基础上,给出系统共形不变性的充要条件,并以此得到共形因子的解析式。利用规范函数满足的Lie结构方程,导出系统相应的新型守恒量形式。

完整系统Tzénoff方程Lie对称性的共形不变性与守恒量

通过完整系统的Tzénoff方程,给出了该系统Tzénoff方程的Lie对称性及其共形不变性的定义,研究了该系统Tzénoff方程Lie对称性的共形不变性及其守恒量,给出了这种守恒量的函数表达式和导出这种守恒量的判据方程,最后给出一个应用实例.

变质量完整系统Tzénoff方程Mei对称性的共形不变性与守恒量

针对变质量的完整约束力学系统建立了相应的Tzénoff方程,给出了Tzénoff方程Mei对称性共形不变性成立时所需的条件,进一步研究了Mei对称性共形不变性所能导出的守恒量,得到了直接用Tzénoff函数来表达的该守恒量的表达式和能够导出这种守恒量的判定方程,最后用实例来说明研究结果的应用.

单面完整约束系统Tzénoff方程Mei对称性的共形不变性与守恒量

研究了单面完整约束系统Tzénoff方程Mei对称性的共形不变性及其守恒量,在给出Mei对称性定义和判据方程的基础上,进一步给出了系统Mei对称性共形不变性的定义和判据方程,并分析了二者的关系.探究了单面完整约束系统Tzénoff方程Mei对称性共形不变性存在守恒量的条件,导出了存在守恒量的结构方程及其守恒量的具体形式.

广义Hamilton系统的共形不变性与Hojman守恒量

研究了广义Hamilton系统在无限小变换下的共形不变性,推导出共形不变性的确定方程,找到在无限小变换下的共形不变性并且是Lie对称性的共形因子,最后导出广义Hamilton系统的运动微分方程共形不变时的Hojman守恒量,并给出应用算例.

非完整系统Hamilton正则方程的形式不变性

研究非完整系统Hamilton正则方程的形式不变性 ,给出形式不变性的定义和判据 ,建立形式不变性和系统守恒量之间的关系 。

Lagrange系统的共形不变性与Hojman守恒量

研究了一般完整Lagrange系统在无限小变换下的共形不变性,推导出共形不变性的确定方程,并且找到在特殊无限小变换下的共形不变性并且是Lie对称性的共形因子,接下来导出Lagrange系统的运动微分方程共形不变时的Hojman守恒量,并给出应用算例.

完整系统Appell方程Mei对称性的共形不变性与守恒量

研究完整系统Appell方程Mei对称性的共形不变性与守恒量.引入无限小单参数变换群及其生成元向量,定义完整系统动力学方程的Mei对称性和共形不变性,给出该系统Mei对称性共形不变性的确定方程.利用规范函数满足的结构方程导出系统相应的Mei守恒量.举例说明结果的应用.

完整系统Appell方程Lie对称性的共形不变性与Hojman守恒量

研究完整系统Appell方程Lie对称性的共形不变性与Hojman守恒量.在时间不变的特殊无限小变换下,定义完整系统动力学方程的Lie对称性和共形不变性,给出该系统Lie对称性共形不变性的确定方程及系统的Hojman守恒量,并举例说明结果的应用.

相对运动动力学Chetaev型非完整系统Appell方程Mei对称性共形不变性和守恒量

在相对运动动力学Chetaev型非完整系统Appell方程Mei对称性的基础上,进一步研究它的共形不变性及其相应的Mei守恒量.利用引入无限小变换群及其生成元向量,定义该系统Appell方程Mei对称性和Mei对称性的共形不变性,推导出该系统具有Mei对称性和Mei对称性共形不变性的充分与必要条件,得到该系统相应的Mei守恒量.最后,举例说明其应用.