CHAPTER I - General Dimensional Theory

Abstract

This chapter focuses on the general dimensional theory. Every phenomenon in mechanics is determined by a series of variables, such as energy, velocity, and stress, which take definite numerical values in several cases. Problems in dynamics or statics reduce to the determination of certain functions and characteristic parameters. The relevant laws of nature and geometrical relations are represented as functional equations, usually differential equations. In purely theoretical investigations, one uses these equations to establish the general qualitative properties of the motion and to calculate the unknown physical variables by means of mathematical analysis. However, it is not always possible to solve a mechanical problem solely by the processes of analysis and calculation; sometimes the mathematical difficulties are too great. Very often the problem can not be formulated mathematically because the mechanical phenomenon to be investigated is too complex to be described by a satisfactory model. This situation arises in many important problems in aeromechanics, hydromechanics, and the theory of structures; in these cases, one has to rely mainly on experimental methods of investigation, to establish the essential physical features of the problem.