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The Principle of Least Action Alberto Rojo (Oakland University, Michigan)

The Principle of Least Action By Alberto Rojo (Oakland University, Michigan)

The Principle of Least Action by Alberto Rojo (Oakland University, Michigan)

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Summary

An accessible introduction to the principle of least action, its history and its fundamental role in science. Including explanations from historical sources, hallmark papers, and worked examples, this is a story that is understandable to those with a less mathematical background, as well as to researchers and students of physics and the history of physics.

The Principle of Least Action Summary

The Principle of Least Action: History and Physics by Alberto Rojo (Oakland University, Michigan)

The principle of least action originates in the idea that, if nature has a purpose, it should follow a minimum or critical path. This simple principle, and its variants and generalizations, applies to optics, mechanics, electromagnetism, relativity, and quantum mechanics, and provides an essential guide to understanding the beauty of physics. This unique text provides an accessible introduction to the action principle across these various fields of physics, and examines its history and fundamental role in science. It includes - with varying levels of mathematical sophistication - explanations from historical sources, discussion of classic papers, and original worked examples. The result is a story that is understandable to those with a modest mathematical background, as well as to researchers and students in physics and the history of physics.

The Principle of Least Action Reviews

'I recommend this exciting book to readers interested in how a small number of principles can explain modern physical theory. A major part of this excellent physical, mathematical, and historical study of the principle of least action is the exposition of the optical-mechanical analogy that led to the invention of Schr dinger's wave mechanics in 1926 ... Containing the mathematical steps of numerous detailed derivations with clearly designed figures to aid the reader, the text is physically and mathematically rigorous and serves as a guide to the next step: the reading of the original papers cited in the references.' Barry R. Masters, Optics & Photonics News

About Alberto Rojo (Oakland University, Michigan)

Alberto Rojo is Associate Professor at Oakland University, Michigan. He is a Fulbright specialist in Physics Education and was awarded the Jack Williams Endowed Chair in Science and Humanities from the University of Eastern New Mexico. His research focuses primarily on theoretical condensed matter and he has previously published books in the popular science field. Anthony Bloch is the Alexander Ziwet Collegiate Professor of Mathematics at the University of Michigan, Ann Arbor. He has received various awards including a Presidential Young Investigator Award, a Guggenheim Fellowship, a Simons Fellowship, and he is Fellow of the Institute of Electrical and Electronics Engineers (IEEE), the Society for Industrial and Applied Mathematics (SIAM), and the American Mathematical Society (AMS). He has served on the editorial boards of various journals and is currently Editor-in-Chief of the SIAM Journal of Control and Optimization.

Table of Contents

1. Introduction; 2. Prehistory of variational principles; 3. An excursio to Newton's Principia; 4. The optical-mechanical analogy, part I; 5. D'Alembert, Lagrange, and the statics-dynamics analogy; 6. The optical mechanical analogy, part II: the Hamilton-Jacobi equation; 7. Relativity and least action; 8. The road to quantum mechanics; Appendix A. Newton's solid of least resistance using calculus; Appendix B. Original statement of D'Alembert's principle; Appendix C. Equations of motion of MacCullagh's ether; Appendix D. Characteristic function for a parabolic Keplerian orbit; Appendix E. Saddle paths for reections on a mirror; Appendix F. Kinetic caustics from quantum motion in one dimension; Appendix G. Einstein's proof of the covariance of Maxwell's equations; Appendix H. Relativistic four vector potential; Appendix I. Ehrenfest's proof of the adiabatic theorem; References; Index.

Additional information

NPB9780521869027
9780521869027
0521869021
The Principle of Least Action: History and Physics by Alberto Rojo (Oakland University, Michigan)
Alberto Rojo (Oakland University, Michigan)
New
Hardback
Cambridge University Press
2018-03-29
266
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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