Dynamic Systems and Control Engineering

In this chapter we will discuss techniques for developing mathematical models of mechanical systems. In doing so, we will take a direct approach to derive governing equations for planar rigid bodies and point masses by first reviewing the equations that describe the behavior of individual mechanical elements and later applying well-known interconnection laws to combine these elements into meaningful representations of physical dynamics. Through this approach, known as mechanical modeling, we will develop mathematical and physical models of mechanical systems with translational, rotational, levered, and geared elements.