Universe Dynamics: The Least Action Principle and Lagrange's Equations

ISBN-13: 9781138335899 / Angielski / Twarda / 2019 / 172 str.

Jacques Vanier; Cipriana Tomescu (Mandache)

Opis

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.

Recenzje

"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

Spis treści

CHAPTER I ■ Introduction CHAPTER II ■ Selected Elements of Classical and Quantum Physics CHAPTER III ■ Search for a Universal Principle CHAPTER IV ■ Selected Applications of Lagrange’s Equations CHAPTER V ■ Fields and Quantum Physics CHAPTER VI ■ Conclusion