Open AccessA new method to obtain first order approximate conserved quantities of second-ordinary dynamics system containing nonlinear perturbation terms
Author(s) -
Lou Zhi-Mei
Publication year - 2014
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.63.060202
Subject(s) - conserved quantity , nonlinear system , perturbation (astronomy) , order (exchange) , physics , mathematical analysis , mathematics , classical mechanics , quantum mechanics , finance , economics
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.