Ordinary Differential Equations through Dimensional Analysis
物理教育
2007-05-23 v1 综合物理
摘要
In in this paper we show how using D.A. it is found a simple change of variables (c.v.) that brings us to obtain differential equations simpler than the original one. In a pedagogical way (at least we try to do that) and in order to make see that each c.v. corresponds to an invariant solution (induced by a symmetry) or a particular solution, we compare (with all the tedious details, i.e. calculations) the proposed method with the Lie method. The method is checked even in ODEs that do not admit symmetries.
引用
@article{arxiv.physics/0502154,
title = {Ordinary Differential Equations through Dimensional Analysis},
author = {José Antonio Belinchón},
journal= {arXiv preprint arXiv:physics/0502154},
year = {2007}
}