含非线性微扰项的二阶动力学系统的一阶近似守恒量的一种新求法  

A new method to obtain first order approximate conserved quantities of second-ordinary dynamics system containing nonlinear perturbation terms

作　　者：楼智美[1] 

机构地区：[1]绍兴文理学院物理系,绍兴312000

出　　处：《物理学报》2014年第6期5-11,共7页Acta Physica Sinica

基　　金：国家自然科学基金重点项目(批准号:10932002)资助的课题~~

摘　　要：从一阶近似守恒量的性质出发,把受微扰系统视为未受微扰系统与微扰项的迭加,提出一种分三步求得一阶近似守恒量的新方法:先选择合适的方法求得未受微扰系统的守恒量I0,再考虑微扰项对守恒量I0的影响,最后利用一阶近似守恒量的性质求得一阶近似守恒量.用该方法研究了一实际的受非线性微扰作用的两自由度动力学系统,得到4个稳定的一阶近似守恒量.用坐标变换法和微扰法得到系统一阶近似解的表达式,并讨论4种特殊情况下的一阶近似解.We consider the perturbed system as the combination of unperturbed system and perturbed term according to the characteristic of the first order approximate conserved quantities, and we suggest a new method to obtain the first order approximate conserved quantities by three steps： first, we select a suitable method to obtain the conserved quantity I0 of unperturbed system, second, we calculate the influence of perturbed terms on conserved quantity I0, and finally we obtain the first order approximate conserved quantities of the system by using the characteristic of the first order approximate conserved quantities. An actual two-dimensional nonlinear dynamics perturbed system is studied in this paper, and four stable first order approximate conserved quantities are obtained by using this new method. The expressions of first order approximate solution of the system are also obtained by transforming coordinates and using the perturbation method, and four special cases are discussed in this paper.

关 键 词：非线性微扰 二阶动力学系统 一阶近似守恒量 坐标变换法 

分 类 号：O316[理学—一般力学与力学基础]