量纲分析的基础及其应用研究

Research on the Basis and Application of Dimensional Analysis

量纲分析是研究物理问题重要方法之一.在研究有关量纲分析的基本理论问题的基础上,提出了关于量纲分析和应用的一些新见解、新方法,引入了量纲式的向量表示法,提出了量纲的幂级数定理和解系定理,有利于从量纲角度来研究复杂的物理问题.

Dimensional analysis is one of the important approaches to study physical problems. On the basis of investigations on the basic theory of dimensional analysis, some new ideas and new methods were presented about the dimensional analysis and their applications. The vector expression of dimensional relations is introduced, and the power series theorem and fundamental solution-set theorem on the dimensional analysis are proposed. The results from this study are beneficial to the investigation on complicated physical problems from the viewpoint of dimensional analysis.