微扰Kepler系统轨道微分方程的近似Lie对称性与近似不变量

Approximate Lie symmetries and approximate invariants of the orbit differential equation for perturbed Kepler system

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。

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.