Structure And Interpretation Of Classical Mechanics

Structure and Interpretation of Classical Mechanics Structure and Interpretation of Classical Mechanics Gerald Jay Sussman and Jack Wisdom with Meinhard E. Mayer The MIT Press Cambridge, Massachusetts London, England c °2000 by The Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. This book was set by the authors using the LATEX typesetting system and was printed and bound in the United States of America. This book is dedicated, in respect and admiration, to The Principle of Least Action. “The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated. In the interest of clearness, it appeared to me inevitable that I should repeat myself frequently, without paying the slightest attention to the elegance of the presentation. I adhered scrupulously to the precept of that brilliant theoretical physicist L. Boltzmann, according to whom matters of elegance ought be left to the tailor and to the cobbler.” Albert Einstein, in Relativity, the Special and General Theory, (1961), p. v. Contents 1 Contents vii Preface xiii Acknowledgments xvii Lagrangian Mechanics 1 1.1 The Principle of Stationary Action 4 1.2 Configuration Spaces 9 1.3 Generalized Coordinates 11 1.4 Computing Actions 16 1.5 The Euler-Lagrange Equations 1.5.1 Derivation of the Lagrange Equations 1.5.2 Computing L