Solution manual for Classical Dynamics of Particles and Systems, 5th Edition, by Thornton

All 14 Chapters Covered
yt yt yt




SOLUTION MANUAL
yt

, Contents




Preface v
Problems Solved in Student Solutions Manual
yt yt yt yt yt vii

1 Matrices, Vectors, and Vector Calculus
yt yt yt yt 1

2 Newtonian Mechanics—Single Particle
yt yt 29

3 Oscillations 79

4 Nonlinear Oscillations and Chaos
yt yt yt 127

5 Gravitation 149

6 Some Methods in The Calculus of Variations
yt yt yt yt yt yt 165

7 Hamilton’s Principle—Lagrangian and Hamiltonian Dynamics
yt yt yt yt 181

8 Central-Force Motion yt 233

9 Dynamics of a System of Particles
yt yt yt yt yt 277

10 Motion in a Noninertial Reference Frame
yt yt yt yt yt 333

11 Dynamics of Rigid Bodies yt yt yt 353

12 Coupled Oscillations
yt 397

13 Continuous Systems; Waves yt yt 435

14 Special Theory of Relativity
yt yt yt 461



iii

,iv CONTENTS

, Preface




This Instructor’s Manual contains the solutions to all the end-of-
yt yt yt yt yt yt yt yt yt



chapter problems (but not the appendices) from Classical Dynamics of Particles and Systems, Fifth
yt yt yt yt yt yt yt yt yt yt yt yt yt yt



Edition, by Stephen T. Thornton and Jerry B. Marion. It is intended for use only by instructors us
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt



ing Classical Dynamics as a textbook, and it is not available to students in any form. A Student Sol
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt



utions Manual containing solutions to about 25% of the end-of-
yt yt yt yt yt yt yt yt yt



chapter problems is available for sale to students. The problem numbers of those solutions in the
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt



Student Solutions Manual are listed on the next page.
yt yt yt yt yt yt yt yt



As a result of surveys received from users, I continue to add more worked out examples in t
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt



he text and add additional problems. There are now 509 problems, a significant number over the
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt



4th edition.
yt yt



The instructor will find a large array of problems ranging in difficulty from the simple “plu
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt



g and chug” to the type worthy of the Ph.D. qualifying examinations in classical mechanics. A fe
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt



w of the problems are quite challenging. Many of them require numerical methods. Having this
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt



solutions manual should provide a greater appreciation of what the authors intended to accomp
yt yt yt yt yt yt yt yt yt yt yt yt yt



lish by the statement of the problem in those cases where the problem statement is not completel
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt



y clear. Please inform me when either the problem statement or solutions can be improved. Spec
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt



ific help is encouraged. The instructor will also be able to pick and choose different levels of diffi
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt



culty when assigning homework problems. And since students may occasionally need hints to
yt yt yt yt yt yt yt yt yt yt yt yt yt



work some problems, this manual will allow the instructor to take a quick peek to see how the st
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt



udents can be helped. yt yt yt



It is absolutely forbidden for the students to have access to this manual. Please do not giv
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt



e students solutions from this manual. Posting these solutions on the Internet will result in wides
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt



pread distribution of the solutions and will ultimately result in the decrease of the usefulness of
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt



the text. yt



The author would like to acknowledge the assistance of Tran ngoc Khanh (5th edition), Wa
yt yt yt yt yt yt yt yt yt yt yt yt yt yt



rren Griffith (4th edition), and Brian Giambattista (3rd edition), who checked the solutions of pre
yt yt yt yt yt yt yt yt yt yt yt yt yt yt



vious versions, went over user comments, and worked out solutions for new problems.
yt yt yt yt yt yt yt yt yt yt yt yt



Without their help, this manual would not be possible. The author would appreciate receiving re
yt yt yt yt yt yt yt yt yt yt yt yt yt yt



ports of suggested improvements and suspected errors. Comments can be sent by email to stt@v
yt yt yt yt yt yt yt yt yt yt yt yt yt yt



irginia.edu, the more detailed the better. yt yt yt yt yt



Stephen T. Thornton yt yt



Charlottesville, Virginia yt




v