微扰力系统一阶近似守恒量与对称性研究

发布时间：2018-12-28 10:03

【摘要】：提出了用泊松括号求一阶近似守恒量的方法,将微扰力学系统的Hamilton函数看成是未受微扰作用系统的Hamilton函数和微扰项两部分组成.先根据未受微扰作用力学系统的特点选择一种合适的方法求得其精确守恒量,再利用泊松括号和偏微分方程的性质求得守恒量的一阶微扰项,最后根据Noether对称性、Lie对称性和Mei对称性性质,求得与一阶近似守恒量相应的一阶近似Noether对称性、近似Lie对称性和近似Mei对称性.研究了受微扰作用的二维各向同性谐振子的一阶近似守恒量和近似对称性,得到了系统的3个一阶近似守恒量及它们相应的一阶近似对称性.结果表明,与3个一阶近似守恒量相应的一阶近似对称性既是近似Noether对称性,又是近似Lie对称性,也是近似Mei对称性.
[Abstract]:In this paper, a Poisson bracket method is proposed to calculate the first order approximate conserved quantity. The Hamilton function of the perturbation mechanics system is regarded as the Hamilton function and the perturbation term of the system without perturbation. According to the characteristics of unperturbed mechanical system, an appropriate method is chosen to obtain the exact conserved quantity, then the first order perturbation term of the conserved quantity is obtained by using the properties of Poisson parentheses and partial differential equations. Finally, according to the Noether symmetry, the first order perturbation term of the conserved quantity is obtained. The properties of Lie symmetry and Mei symmetry are obtained. The first order approximate Noether symmetry, approximate Lie symmetry and approximate Mei symmetry corresponding to the first order approximate conserved quantity are obtained. The first order approximate conserved quantity and approximate symmetry of two-dimensional isotropic harmonic oscillator subjected to perturbation are studied. Three first order approximate conserved quantities and their corresponding first order approximate symmetries are obtained. The results show that the first order approximate symmetry corresponding to the three first order approximate conserved quantities is not only approximate Noether symmetry, but also approximate Lie symmetry and approximate Mei symmetry.
【作者单位】：绍兴文理学院物理系;
【基金】：国家自然科学基金(11472177)
【分类号】：O316

【相似文献】