文档介绍：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 pay-
ing 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
Contents vii
Preface xiii
Acknowledgments xvii
1 Lagrangian Mechanics 1
The Principle of Stationary Action 4
Configuration Spaces 9
Generalized Coordinates 11
Actions 16
The Euler-Lagrange Equations 26
Derivation of the Lagrange Equations 27
Lagrange’s Equations 34
How to Find Lagrangians 37
Coordinate Transformations 44
Systems with Rigid Constraints 48
Constraints as Coordinate Transformations 60
The Lagrangian is Not Unique 62
Evolution of Dynamical State 67
Conserved Quanti