Introduction

In this chapter, the balance law F = ma for a single particle plays a central role. This law is then used to examine models for several physical systems ranging from planetary motion to a model for a roller coaster. Our discussion of the behavior of these systems predicted by the models relies heavily on numerical integration of the equations of motion provided by F = ma, and it is presumed that the reader is familiar with the numerical integration of ordinary differential equations.

Two of the most important types of forces featured in many applications are conservative forces and constraint forces. For the former, the gravitational force between two particles is the prototypical example, whereas the most common constraint force in particle mechanics is the normal force. It is crucial to be able to properly formulate and represent conservative and constraint forces, and we will spend a considerable amount of time discussing them in this chapter. In contrast to most texts in dynamics, here we consider friction forces to be types of constraint forces.

For most applications, exact (or analytical) solutions are not available and recourse to numerical methods is often the only course of action. In validating these solutions, any conservations that might be present are crucial. To this end, conservations of momentum and energy are discussed at length and we also show (with the help of two examples) how angular momentum conservation can often be exploited.