2.3 Mathematical Modeling

A mathematical model is an algorithm or a set of equations that represents the interesting behavior of a system. Experts with thorough knowledge of the system and its interaction with the environment typically perform model creation tasks in development projects for complex dynamic systems. The development of a model for a complex dynamic system is an iterative process that involves significant effort to verify the correctness and accuracy of the resulting implementation.

The process of model development begins with a specification of the requirements the model must meet. The following are issues that must be addressed in developing a model of a complex system.

What effects should be included in the model? A system may exhibit many different kinds of behavior (for example, the motion of motors, vibration, wear of moving parts, etc.), but not all of these behaviors need to be modeled to produce an effective simulation. Limiting the effects modeled to only those that are truly necessary will make the model less complex and easier to build, test, and maintain as well as requiring less computational resources to execute.

How detailed must the model be? In many cases, a simple model is all that is needed, but if precise determination of system behavior is required, the model may need to be very elaborate.

What interactions between the system and the outside environment must be modeled? For example, a communication satellite motion model must operate in conjunction with a model of the earth's gravitational field,...