https://oxford.universitypressscholarship.com/view/10.1093/oso/9780198743040.001.0001/oso-9780198743040 We use cookies to enhance your experience on our website. By continuing to use our website, you are agreeing to our use of cookies. You can change your cookie settings at any time.Find out more Jump to ContentJump to Main Navigation OSO version 0.4.3 build 1 University Press Scholarship Online * Sign in. * Not registered? Sign up. * About * News * Partner Presses * Subscriber Services * Contact Us * Take a Tour * Help Oxford Scholarship Online Publications Pages * Publications * Pages University Presses (*)All Partner Presses ( )Oxford Scholarship Online Advanced Search [ ] [Search] Help * Browse by Subject + Archaeology + Biology + Business and Management + Chemistry + Classical Studies + Clinical Medicine and Allied Health + Computer Science + Earth Sciences and Geography + Economics and Finance + Education + Environmental Science + History + Law + Linguistics + Literature + Mathematics + Music + Neuroscience + Palliative Care + Philosophy + Physics + Political Science + Psychology + Public Health and Epidemiology + Religion + Social Work + Sociology * My Content (0) Recently viewed (0) + Save Entry * My searches (0) Recently viewed (0) + Save Search The Lazy Universe - An Introduction to the Principle of Least Action - Oxford Scholarship Online Users without a subscription are not able to see the full content. * Find in Worldcat The Lazy Universe: An Introduction to the Principle of Least Action Jennifer Coopersmith Abstract Action and the Principle of Least Action are explained: what Action is, why the Principle of Least Action works, why it underlies all physics, and what are the insights gained into energy, space, and time. The physical and mathematical origins of the Lagrange Equations, Hamilton's Equations, the Lagrangian, the Hamiltonian, and the Hamilton-Jacobi Equation are shown. Also, worked examples in Lagrangian and Hamiltonian Mechanics are given. However the aim is to explain physics rather than to give a technical mastery of the subject. Therefore, much of the mathematics is in the appendices. While ... More Action and the Principle of Least Action are explained: what Action is, why the Principle of Least Action works, why it underlies all physics, and what are the insights gained into energy, space, and time. The physical and mathematical origins of the Lagrange Equations, Hamilton's Equations, the Lagrangian, the Hamiltonian, and the Hamilton-Jacobi Equation are shown. Also, worked examples in Lagrangian and Hamiltonian Mechanics are given. However the aim is to explain physics rather than to give a technical mastery of the subject. Therefore, much of the mathematics is in the appendices. While there is still some mathematics in the main text, the reader may select whether to work through, skim-read, or skip over it: the "story-line" will just about be maintained whatever route is chosen. The work is a much-reduced and simplified version of the outstanding text, "The Variational Principles of Mechanics" written by Cornelius Lanczos in 1949. That work is barely known today, and the present work may be considered as a tiny stepping-stone toward it. A principle that underlies all of physics will have wider repercussions; it is also to be appreciated in an aesthetic sense. It is hoped that this book will lead the reader to the widest possible understanding of the Principle of Least Action. Ideas such as Variational Mechanics, phase space, Fermat's Principle, and Noether's Theorem are explained. Keywords: Least Action, Lagrangian Mechanics, Hamiltonian Mechanics, Variational Mechanics, Cornelius Lanczos, Hamilton-Jacobi Equation, phase space, Fermat's Principle, Noether's Theorem Bibliographic Information Print publication date: 2017 Print ISBN-13: 9780198743040 Published to Oxford Scholarship DOI:10.1093/oso/ Online: June 2017 9780198743040.001.0001 Authors Affiliations are at time of print publication. Jennifer Coopersmith, author Honorary Research Associate, La Trobe University, Australia More Less * Print * Save * Cite * Email this content Share Link ----------------------------------------------------------------- Copy this link, or click below to email it to a friend Email this content or copy the link directly: [https://oxford.unive] The link was not copied. Your current browser may not support copying via this button. Link copied successfully Copy link ----------------------------------------------------------------- * Share This Decrease Increase Search within book [ ] [GO] Subscriber sign in You could not be signed in, please check and try again. Username [ ] Please enter your Username Password [ ] Please enter your Password Forgot password? [Login] You could not be signed in, please check and try again. Sign in with your library card [ ] Please enter your library card number [Sign in] * Login with your Library Card * Sign in via your Institution * Login with Athens Don't have an account? Subject(s) in Oxford Scholarship Online * History of Physics * Particle Physics / Astrophysics / Cosmology * Physics Show Summary Details subscribe or login to access all content. Subscriber Login Email Address [ ] Please enter your Username Password [ ] Please enter your Password [Login] Forgot password? Library Card # [ ] Please enter your library card number [Login] * Login with your Library Card * Sign in via your Institution * Login with Athens Don't have an account? Contents Go to page: [ ] [Go] View: * no detail * some detail * full detail Front Matter Title Pages Frontispiece Dedication Epigraph Preface List of Figures 1 Introduction 2 Antecedents 3 Mathematics and physics preliminaries: of hills and plains and other things 4 The Principle of Virtual Work 5 D'Alembert's Principle 6 Lagrangian Mechanics 7 Hamiltonian Mechanics 8 The whole of physics 9 Final words End Matter Appendix A1.1 Newton's Laws of Motion Appendix A2.1 Portraits of the physicists Appendix A3.1 Reversible displacements Appendix A6.1 Worked examples in Lagrangian Mechanics Appendix A6.2 Proof that T is a function of v2 Appendix A6.3 Energy conservation and the homogeneity of time Appendix A6.4 The method of Lagrange Multipliers Appendix A6.5 Generalized Forces Appendix A7.1 Hamilton's Transformation, examples Appendix A7.2 Demonstration that the pi s are independent coordinates Appendix A7.3 Worked examples in Hamiltonian Mechanics Appendix A7.4 Incompressibility of the phase fluid Appendix A7.5 Energy conservation in extended phase space Appendix A7.6 Link between the action, S, and the 'circulation' Appendix A7.7 Transformation equations linking p and q via S Appendix A7.8 Infinitesimal canonical transformations Appendix A7.9 Perpendicularity of wavefronts and rays Appendix A7.10 Problems solved using the Hamilton-Jacobi Equation Appendix A7.11 Quasi refractive index in mechanics Appendix A7.12 Einstein's link between Action and the de Broglie waves Bibliography and Further Reading Index Oxford University Press Copyright (c) 2022. All rights reserved. PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use.date: 29 March 2022 * Cookie Policy * Privacy Policy * Legal Notice * Credits * Accessibility Powered by: Safari Books Online * [68.37.28.109] * 68.37.28.109 *