E-Book Overview
Would give zero stars, but it is not possible. To use the book, you need specific version of Scheme language with specific library. These are available only for Linux or MacOS. Since I don't own Linux or Mac machine and don't plan to own one, I stopped reading the book on page 3 and never resumed. Unfortunately, I discovered this after 30 days return period. By the way, link to this software, listed in the book is wrong. There should be a big warning on the cover that software is available only for Linus and MacOS, to avoid situations like mine. Selling book with software that runs on 10% of computers, without visible warning should be considered a fraud. Oh, yes, you can google and find variuos ad-hoc procedures to run this on Windows, but none of these worked for me.
E-Book Content
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 Lagrange’s Equations
26 27 34
1.6 1.6.1 1.6.2 1.6.3 1.6.4
How to Find Lagrangians Coordinate Transformations Systems with Rigid Constraints Constraints as Coordinate Transformations The Lagrangian is Not Unique
37 44 48 60 62
1.7
Evolution of Dynamical State
67
1.8 1.8.1 1.8.2 1.8.3 1.8.4
Conserved Quantities Conserved Momenta Energy Conservation Central Forces in Three Dimensions Noether’s Theorem
76 76 78 81 84
1.9
Abstraction of Path Functions
88
1.10 Constrained Motion 1.10.1Coordinate Constraints
93 95
viii
2
3
Contents
1.10.2Derivative Constraints 1.10.3Non-Holonomic Systems
102 106
1.11 Summary
109
1.12 Projects
110
Rigid Bodies
113
2.1
Rotational Kinetic Energy
114
2.2
Kinematics of Rotation
116
2.3
Moments of Inertia
118
2.4
Inertia Tensor
121
2.5
Principal Moments of Inertia
123<