Introduction to Structural Approach — Overview of the Book

Abstract

This chapter is a brief introduction to the central ideas of the combinatorial method of this book for the structural analysis of engineering systems. We explain the motivations and the general framework by referring, as a specific example, to the problem of computing the index of a system of differentialalgebraic equations (DAEs). In this approach, engineering systems are described by mixed polynomial matrices. A kind of dimensional analysis is also invoked. It is emphasized that relevant physical observations are crucial to successful mathematical modeling for structural analysis. Though the DAEindex problem is considered as an example, the methodology introduced here is more general in scope and is applied to other problems in subsequent chapters.