Perfect Form: Variational Principles, Methods, and Applications in Elementary Physics

Abstract

This short book is concerned with the physical applications of variational principles of the calculus. It is intended for undergraduate students who have taken some introductory lectures on the subject and have been exposed to Lagrangian and Hamiltonian mechanics. Throughout the book the author emphasizes the historical background to the subject and provides numerous problems, mainly from the fields of mechanics and optics. Some of these problems are provided with an answer, while others, regretfully, are not. It would have been an added help to the undergraduate reader if complete solutions could have been provided in an appendix. The introductory chapter is concerned with Fermat's Principle and image formation. This is followed by the derivation of the Euler - Lagrange equation. The third chapter returns to the subject of optical paths without making the link with a mechanical variational principle - that comes later. Chapters on the subjects of minimum potential energy, least action and Hamilton's principle follow. This volume provides an `easy read' for a student keen to learn more about the subject. It is well illustrated and will make a useful addition to all undergraduate physics libraries.