ALL 6 CHAPTERS COVERED
, Solutions to the Exercises
in
Essentials of Hamiltonian Dynamics
John H. Lowenstein
,Solutions to the Exercises Essentials of Hamiltonian Dynamics
Preface
This electronic book contains solutions to all of the exercises included in
Essentials of Hamiltonian Dynamics (Cambridge University Press, 2012). I
am providing it free of charge to authorized instructors via the publisher’s
website, with the hope that it will enhance the pedagogical value of the
textbook. In this solutions book, references to formulas, figures, and citations
in the textbook are prefaced with the initials “EHD”.
The page numbers and subjects of the exercise solutions are listed at the
beginning of each chapter. Those requiring computer assistance have been
prepared as Mathematicar notebooks, and this is indicated in the lists by the
notation (M). Those based on traditional methods of mathematical analysis
have been prepared as LaTeX documents and are denoted by (L).
The presence of exercises and illustrative examples requiring the use of
mathematical software (not necessarily Mathematica) is a special feature of
the textbook. Students who wish quickly to get up to speed with Mathemat-
ica will find that the latter comes equipped with excellent documentation. In
addition, they may find useful a brief downloadable manual which I prepared
as a supplementary resource for readers of the textbook.
One advantage of the electronic format is that updates can be provided
when needed. Please email your suggestions for improvements and correc-
tions to me at . An Errata file will be maintained
on the Cambridge University Press website so that confusing errors in the
textbook can quickly be brought to the attention of instructors and their
students.
John H. Lowenstein
CONTENTS
Chapter 1 Fundamentals of classical dynamics 2
Chapter 2 The Hamiltonian formalism 35
Chapter 3 Integrable systems 62
Chapter 4 Canonical perturbation theory 104
Chapter 5 Order and chaos in Hamiltonian systems 116
Chapter 6 The swing-spring 155
1
, Solutions to the Exercises Essentials of Hamiltonian Dynamics
Chapter 1 Fundamentals of classical dynamics
CONTENTS
1.1 Simple pendulum separatrix (L) 3
1.2 Simple pendulum plots (M) 5
1.3 Simple pendulum period (L) 6
1.4 Simple pendulum, E > g (L) 7
1.5 Morse potential (M, L) 8
1.6 Elastic pendulum (L) 21
1.7 Cycloid (L, M) 22
1.8 Bead on a rotating loop (M) 26
1.9 Chaotic bead on a loop (M) 27
1.10 Independence of top integrals (L) 29
1.11 Symmetric top orbits (L) 30
L = LaTeX document, M= Mathematica notebook
Chapter 1 2
, Solutions to the Exercises
in
Essentials of Hamiltonian Dynamics
John H. Lowenstein
,Solutions to the Exercises Essentials of Hamiltonian Dynamics
Preface
This electronic book contains solutions to all of the exercises included in
Essentials of Hamiltonian Dynamics (Cambridge University Press, 2012). I
am providing it free of charge to authorized instructors via the publisher’s
website, with the hope that it will enhance the pedagogical value of the
textbook. In this solutions book, references to formulas, figures, and citations
in the textbook are prefaced with the initials “EHD”.
The page numbers and subjects of the exercise solutions are listed at the
beginning of each chapter. Those requiring computer assistance have been
prepared as Mathematicar notebooks, and this is indicated in the lists by the
notation (M). Those based on traditional methods of mathematical analysis
have been prepared as LaTeX documents and are denoted by (L).
The presence of exercises and illustrative examples requiring the use of
mathematical software (not necessarily Mathematica) is a special feature of
the textbook. Students who wish quickly to get up to speed with Mathemat-
ica will find that the latter comes equipped with excellent documentation. In
addition, they may find useful a brief downloadable manual which I prepared
as a supplementary resource for readers of the textbook.
One advantage of the electronic format is that updates can be provided
when needed. Please email your suggestions for improvements and correc-
tions to me at . An Errata file will be maintained
on the Cambridge University Press website so that confusing errors in the
textbook can quickly be brought to the attention of instructors and their
students.
John H. Lowenstein
CONTENTS
Chapter 1 Fundamentals of classical dynamics 2
Chapter 2 The Hamiltonian formalism 35
Chapter 3 Integrable systems 62
Chapter 4 Canonical perturbation theory 104
Chapter 5 Order and chaos in Hamiltonian systems 116
Chapter 6 The swing-spring 155
1
, Solutions to the Exercises Essentials of Hamiltonian Dynamics
Chapter 1 Fundamentals of classical dynamics
CONTENTS
1.1 Simple pendulum separatrix (L) 3
1.2 Simple pendulum plots (M) 5
1.3 Simple pendulum period (L) 6
1.4 Simple pendulum, E > g (L) 7
1.5 Morse potential (M, L) 8
1.6 Elastic pendulum (L) 21
1.7 Cycloid (L, M) 22
1.8 Bead on a rotating loop (M) 26
1.9 Chaotic bead on a loop (M) 27
1.10 Independence of top integrals (L) 29
1.11 Symmetric top orbits (L) 30
L = LaTeX document, M= Mathematica notebook
Chapter 1 2
