Chapters 2–8 focused on a single objective: finding the equations governing the motion of a system consisting of particles and rigid bodies, a process commonly known as mathematical modeling. Nonetheless, while models constitute the fundamental basis upon which everything else is built, the process of fully understanding and controlling the dynamic behavior of a system cannot be fully realized without analyzing its response, a process commonly known as mathematical analysis.

As you may have noticed in the previous chapters, models of particles and rigid bodies in motion are described by one or more non-linear ordinary differential equations. As...