Lagrangian and Hamiltonian Mechanics - José Rachid Mohallem

Lagrangian and Hamiltonian Mechanics

A Modern Approach with Core Principles and Underlying Topics
Buch | Hardcover
XI, 142 Seiten
2024 | 2024
Springer International Publishing (Verlag)
978-3-031-55201-4 (ISBN)
80,24 inkl. MwSt

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. Infact, 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.

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).

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

Erscheinungsdatum
Zusatzinfo XI, 142 p. 23 illus., 2 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Naturwissenschaften Physik / Astronomie Mechanik
Schlagworte Adiabatic Invariants • Equivalent Lagrangians • Galilean invariance • Hamilton-Jacobi theory • Hamilton's Principle of Least Action • Lagrange Equations from D'Alembert's Principle • Newton's Laws in Lagrangian Mechanics • Noether's Theorem • Poisson Brackets • Rigid Body Motion
ISBN-10 3-031-55201-6 / 3031552016
ISBN-13 978-3-031-55201-4 / 9783031552014
Zustand Neuware
Haben Sie eine Frage zum Produkt?
Mehr entdecken
aus dem Bereich

von Tilo Arens; Frank Hettlich; Christian Karpfinger …

Buch | Hardcover (2022)
Springer Spektrum (Verlag)
79,99