Lagrangian and Hamiltonian Mechanics

Chapter 1: Fundamentals.- Chapter 2: Lagrangian mechanics with L = T – V.- Chapter 3: Hamiltonian mechanics.- Chapter 4: Lagrangian and Hamiltonian introduction of field theory.

Dr. José R. Mohallem has served as a professor of physics at the Federal University of Minas Gerais in Belo Horizonte, Brazil since 1981. He has decades of experience teaching classical and quantum mechanics and has research expertise in atomic and molecular physics. Since 1988, he has been a research fellow for the Conselho Nacional de Pesquisas Científicas e Tecnológicas (CNPq). Previously, he has also served as an invited senior researcher at Queen's University (Belfast, UK), visiting professor at the University of Reims Champagne-Ardenne (Reims, France), and a director of research at the French National Center for Scientific Research (Paris, France).

This book serves as a textbook for an analytical mechanics course, a fundamental subject of physics, that pays special attention to important topics that are not discussed in most standard textbooks. Readers are provided with a clear understanding of topics that are usually inaccessible to the undergraduate level and that are critical to learning Lagrangian and Hamiltonian mechanics. Each chapter also includes worked problems and solutions, as well as additional exercises for readers to try.  This book begins with the fundamentals of analytical mechanics, concisely introducing readers to the calculus of variations, Hamilton’s Principle, and Lagrange’s equations. While presenting readers with these core topics, the author uses an intuitive approach to delve into essential questions, such as where Galilean invariance lies in Lagrangian mechanics and how Hamilton’s Principle of Least Action encompasses Newton’s three laws, interesting conclusions that often go unnoticed. In fact, Hamilton’s principle is taken throughout as the very origin of classical physical laws, and the choice of appropriate Lagrangians in each case as the real theoretical challenge, meaning that forms of Lagrangian which differ from the standard one are not mere curiosities but, instead, the general rule.
This book clarifies common misunderstandings that students face when learning the subject and formally rationalizes concepts that are often difficult to grasp. In addition, the final chapter provides an introduction to a Lagrangian field theory for those interested in learning more advanced topics. Ideal for upper undergraduate and graduate students, this book seeks to teach the intrinsic meaning of the principles and equations taught in an analytical mechanics course and convey their usefulness as powerful theoretical instruments of modern physics.

Discusses fundamental issues and special topics that are absent in standard textbooks Obtain all results from Hamilton’s principle and appropriate guessed Lagrangians Includes problems and solutions that are accessible to students of all levels