Open AccessApproximate Lie symmetries and approximate invariants of the orbit differential equation for perturbed Kepler system
Author(s) -
Lou Zhi-Mei
Publication year - 2010
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.59.6764
Subject(s) - homogeneous space , orbit (dynamics) , kepler problem , differential equation , invariant (physics) , lie group , kepler , physics , circular orbit , mathematical physics , mathematics , mathematical analysis , pure mathematics , classical mechanics , astrophysics , geometry , planet , engineering , aerospace engineering
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.