1st Edition

Universe Dynamics The Least Action Principle and Lagrange’s Equations

    184 Pages 36 B/W Illustrations
    by CRC Press

    184 Pages 36 B/W Illustrations
    by CRC Press

    CHOICE Recommended Title, June 2019

    Brought together in one focused and exclusive treatment, this book provides an elementary introduction to the important role and use of the least action principle and the resulting Lagrange’s equations in the analysis of the laws that govern the universe. It is an ideal complimentary resource to accompany undergraduate courses and textbooks on classical mechanics.


    • Uses mathematics accessible to beginners
    • Brings together the Principle of Least Action, Lagrange's equations, and variational principles in mechanics in one cohesive text
    • Written in a clear and easy-to-understand manner

    Chapter 1: Introduction

    Chapter 2: Selected Elements of Classical and Quantum Physics

    Chapter 3: Search for a Universal Principle

    Chapter 4: Selected Applications of Lagrange’s Equations

    Chapter 5: Fields and Quantum Physics

    Chapter 6: Conclusion


    Jacques Vanier is an adjunct professor in the Physics Department at the University of Montreal. He is a fellow of the Royal Society of Canada, the American Physical Society, and the Institute of Electrical and Electronic Engineers. He has written more than 120 journal articles and proceedings papers and is the author of several books on masers, lasers, and atomic frequency standards. He has written a book on the physics of the universe in simple language for the general public. He was professor of physics at Laval University where he gave courses on general physics. His research work is oriented toward the understanding and application of quantum electronics phenomena.

    Cipriana Tomescu is an invited researcher in the Physics Department at the University of Montreal. She is the author of numerous articles in scientific journals and conference proceedings. She is the co-author with Dr. Vanier of a book on atomic frequency standards. In her career, she has worked in several institutions around the world as an invited researcher. Her research involves state-of-the-art microwave and optical atomic frequency standards.

    "In the preface and introduction to this text, Vanier and Tomescu (both, Univ. of Montreal) rightfully argue that much can be learned about dynamics in all areas of physics through the application of the least action principle. Despite this fact, most undergraduate curricula limit the discussion of this principle to just part of an upper-division mechanics course. The aim of this text is to remedy that.
    Before looking at the principle of least action, the text presents a review of mechanics, relativity, electromagnetism, and quantum mechanics. The authors' aim in this section is to see how these areas are typically studied without the use of the least action principle. The principle is then presented and tied directly to Lagrange’s equations. The second half of the text consists of various examples of applying the principle to the areas that were discussed in the initial review. Though not all problems of interest are considered, these are good examples that can be used to see how to apply the principle broadly. This is not an introductory text; it assumes a familiarity with differential calculus and is probably best suited for upper-division undergraduates.
    Summing Up: Recommended. Advanced undergraduates and graduate students."
    —E. Kincanon, Gonzaga University in CHOICE, June 2019