ABSTRACT
This chapter presents several commonly used forms in the representation of mathematical models of dynamic systems. The main topics covered in this chapter include the configuration form, state-space form, input–output (I/O) equation, transfer function, and block diagram representation. Also included is how any one of these forms may be obtained from any other form. A set of coordinates that completely describes the motion of a system is known as a set of generalized coordinates. This set is not unique, so that more than one set of coordinates can be chosen for the same system. Dynamic systems, ranging from mechanical to fluid and thermal systems, are mathematically modeled as systems of ordinary differential equations (ODEs) of various orders. One of the most convenient forms is achieved by transforming a system of ODEs of various orders into a larger system of first-order ODEs.
