2.1 Introduction

To develop a simulation of an interesting and complex dynamic system, one must begin by developing mathematical models of the system components and the interactions between the system and its operational environment. A mathematical model is an algorithm or a set of equations and a set of related data values that together represent the significant behavior of a system, process, or phenomenon.

Depending on the system to be modeled, the development of a representative set of mathematical models may be an easy task or it may require a great deal of work. In cases where the system's dynamics are not well understood, it will be necessary for the developer to design and execute a series of experiments to collect data that can be used for model development.

This chapter introduces concepts involved in the mathematical modeling of dynamic systems and presents some of the basic techniques used in their development. The relevant properties of dynamic systems will be examined and I will provide examples of engineering techniques for deriving mathematical representations of their behavior. The positive and negative attributes of commonly used modeling approaches will also be discussed.