文献类型：期刊文献

中文题名：微扰Kepler系统轨道微分方程的近似Lie对称性与近似不变量

英文题名：Approximate Lie symmetries and approximate invariants of the orbit differential equation for perturbed Kepler system

作者：楼智美[1]

机构：[1]绍兴文理学院物理系

年份：2010

期号：10

起止页码：6764

中文期刊名：物理学报

外文期刊名：Acta Physica Sinica

收录：SCI-EXPANDED(收录号：WOS:000283406400009)、CSTPCD、、Scopus、CSCD2011_2012、北大核心2008、WOS、北大核心、CSCD

语种：中文

中文关键词：微扰Kepler系统轨道微分方程;近似Lie对称性;近似不变量

外文关键词：orbit differential equation for perturbed Kepler system; approximate Lie symmetries; approximate invariants

中文摘要：把极角θ视为独立变量,得到Kepler系统的轨道微分方程.首先讨论Kepler系统轨道微分方程的Lie对称性和不变量,微扰Kepler系统轨道微分方程的精确Lie对称性和精确不变量,其次讨论微扰Kepler系统轨道微分方程的近似Lie对称性和近似不变量,并得到了微扰Kepler系统的9个一阶近似Lie对称性和6个一阶近似不变量,其中1个实为精确不变量,而其余5个分别等于微扰系数ε乘以Kepler系统相应的5个不变量。

外文摘要：We obtained the orbit differential equation of Kepler system when the θ is the independent variable.The Lie symmetries and invariants of the orbit differential equation for Kepler system,the exact Lie symmetries and exact invariants of the orbit differential equation for perturbed Kepler system are discussed firstly.Then we discuss the approximate Lie symmetries and approximate invariants of the orbit differential equation for perturbed Kepler system.Nine first order approximate Lie symmetries and six first order approximate invariants are obtained,one of them is a exact invariant in fact,and the other five of them are equivalent to the corresponding invariants of Kepler system multiplyied by the perturbation coefficient ε.