All 14 Chapters Covered
SOLUTION MANUAL
, Contents
Preface v
Problems Solved in Student Solutions Manual vii
1 Matrices, Vectors, and Vector Calculus 1
2 Newtonian Mechanics—Single Particle 29
3 Oscillations 79
4 Nonlinear Oscillations and Chaos 127
5 Gravitation 149
6 Some Methods in The Calculus of Variations 165
7 Hamilton’s Principle—Lagrangian and Hamiltonian Dynamics 181
8 Central-Force Motion 233
9 Dynamics of a System of Particles 277
10 Motion in a Noninertial Reference Frame 333
11 Dynamics of Rigid Bodies 353
12 Coupled Oscillations 397
13 Continuous Systems; Waves 435
14 Special Theory of Relativity 461
iii
,iv CONTENTS
Preface
This Instructor’s Manual contains the solutions to all the end-of-chapter problems (but not the
appendices) from Classical Dynamics of Particles and Systems, Fifth Edition, by Stephen T.
Thornton and Jerry B. Marion. It is intended for use only by instructors using Classical Dynamics
as a textbook, and it is not available to students in any form. A Student Solutions Manual
containing solutions to about 25% of the end-of-chapter problems is available for sale to
students. The problem numbers of those solutions in the Student Solutions Manual are listed on
the next page.
As a result of surveys received from users, I continue to add more worked out examples in
the text and add additional problems. There are now 509 problems, a significant number over
the 4th edition.
The instructor will find a large array of problems ranging in difficulty from the simple
“plug and chug” to the type worthy of the Ph.D. qualifying examinations in classical mechanics.
A few of the problems are quite challenging. Many of them require numerical methods. Having
this solutions manual should provide a greater appreciation of what the authors intended to
accomplish by the statement of the problem in those cases where the problem statement is not
completely clear. Please inform me when either the problem statement or solutions can be
improved. Specific help is encouraged. The instructor will also be able to pick and choose
different levels of difficulty when assigning homework problems. And since students may
occasionally need hints to work some problems, this manual will allow the instructor to take a
quick peek to see how the students can be helped.
It is absolutely forbidden for the students to have access to this manual. Please do not
give students solutions from this manual. Posting these solutions on the Internet will result in
widespread distribution of the solutions and will ultimately result in the decrease of the
usefulness of the text.
The author would like to acknowledge the assistance of Tran ngoc Khanh (5th edition),
Warren Griffith (4th edition), and Brian Giambattista (3rd edition), who checked the solutions of
previous versions, went over user comments, and worked out solutions for new problems.
Without their help, this manual would not be possible. The author would appreciate receiving
reports of suggested improvements and suspected errors. Comments can be sent by email to
, the more detailed the better.
Stephen T. Thornton
Charlottesville, Virginia
v
, CHAPTER 1
Matrices, Vectors,
and Vector Calculus
1-1.
x1
45˚
x1
45˚
x3
x3
Axes x1 and x3 lie in the x1x3 plane.
The transformation equations are:
x1 = x1 cos 45 − x3 cos 45
x2 = x2
x3 = x3 cos 45 + x1 cos 45
1 1
x = x − x
1 1 3
2 2
x2 = x2
1 1
x = x − x
3 1 3
2 2
So the transformation matrix is:
1 1
0 −
2 2
0 1 0
1 1
0
2 2
1
SOLUTION MANUAL
, Contents
Preface v
Problems Solved in Student Solutions Manual vii
1 Matrices, Vectors, and Vector Calculus 1
2 Newtonian Mechanics—Single Particle 29
3 Oscillations 79
4 Nonlinear Oscillations and Chaos 127
5 Gravitation 149
6 Some Methods in The Calculus of Variations 165
7 Hamilton’s Principle—Lagrangian and Hamiltonian Dynamics 181
8 Central-Force Motion 233
9 Dynamics of a System of Particles 277
10 Motion in a Noninertial Reference Frame 333
11 Dynamics of Rigid Bodies 353
12 Coupled Oscillations 397
13 Continuous Systems; Waves 435
14 Special Theory of Relativity 461
iii
,iv CONTENTS
Preface
This Instructor’s Manual contains the solutions to all the end-of-chapter problems (but not the
appendices) from Classical Dynamics of Particles and Systems, Fifth Edition, by Stephen T.
Thornton and Jerry B. Marion. It is intended for use only by instructors using Classical Dynamics
as a textbook, and it is not available to students in any form. A Student Solutions Manual
containing solutions to about 25% of the end-of-chapter problems is available for sale to
students. The problem numbers of those solutions in the Student Solutions Manual are listed on
the next page.
As a result of surveys received from users, I continue to add more worked out examples in
the text and add additional problems. There are now 509 problems, a significant number over
the 4th edition.
The instructor will find a large array of problems ranging in difficulty from the simple
“plug and chug” to the type worthy of the Ph.D. qualifying examinations in classical mechanics.
A few of the problems are quite challenging. Many of them require numerical methods. Having
this solutions manual should provide a greater appreciation of what the authors intended to
accomplish by the statement of the problem in those cases where the problem statement is not
completely clear. Please inform me when either the problem statement or solutions can be
improved. Specific help is encouraged. The instructor will also be able to pick and choose
different levels of difficulty when assigning homework problems. And since students may
occasionally need hints to work some problems, this manual will allow the instructor to take a
quick peek to see how the students can be helped.
It is absolutely forbidden for the students to have access to this manual. Please do not
give students solutions from this manual. Posting these solutions on the Internet will result in
widespread distribution of the solutions and will ultimately result in the decrease of the
usefulness of the text.
The author would like to acknowledge the assistance of Tran ngoc Khanh (5th edition),
Warren Griffith (4th edition), and Brian Giambattista (3rd edition), who checked the solutions of
previous versions, went over user comments, and worked out solutions for new problems.
Without their help, this manual would not be possible. The author would appreciate receiving
reports of suggested improvements and suspected errors. Comments can be sent by email to
, the more detailed the better.
Stephen T. Thornton
Charlottesville, Virginia
v
, CHAPTER 1
Matrices, Vectors,
and Vector Calculus
1-1.
x1
45˚
x1
45˚
x3
x3
Axes x1 and x3 lie in the x1x3 plane.
The transformation equations are:
x1 = x1 cos 45 − x3 cos 45
x2 = x2
x3 = x3 cos 45 + x1 cos 45
1 1
x = x − x
1 1 3
2 2
x2 = x2
1 1
x = x − x
3 1 3
2 2
So the transformation matrix is:
1 1
0 −
2 2
0 1 0
1 1
0
2 2
1
