1 - Fundamental concepts

Summary

This book is about Lagrangians and Hamiltonians. To state it more formally, this book is about the variational approach to analytical mechanics. You may not have been exposed to the calculus of variations, or may have forgotten what you once knew about it, so I am not assuming that you know what I mean by, “the variational approach to analytical mechanics.” But I think that by the time you have worked through the first two chapters, you will have a good grasp of the concept.

We being with a review of introductory concepts and an overview of background material. Some of the concepts presented in this chapter will be familiar from your introductory and intermediate mechanics courses. However, you will also encounter several new concepts that will be useful in developing an understanding of advanced analytical mechanics.

Kinematics

A particle is a material body having mass but no spatial extent. Geometrically, it is a point. The position of a particle is usually specified by the vector r from the origin of a coordinate system to the particle. We can assume the coordinate system is inertial and for the sake of familiarity you may suppose the coordinate system is Cartesian. See Figure 1.1.