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Tables of Contents for The Genesis of Simulation in Dynamics
Chapter/Section Title
Page #
Page Count
Preface
vii
6
List of Figures
xiii
Introduction
1
6
Part I: History
7
96
1. The FPU Model and Simulation: "A Little Discovery"
9
22
1.1. Development
9
2
1.2. Dynamics to Statistical Mechanics
11
2
1.3. Surfaces of Constraint
13
2
1.4. Global Versus Local Analysis
15
1
1.5. Simulation
15
1
1.6. Loading the Nonlinear String
16
3
1.7. Modal Representation
19
2
1.8. Model Considerations
21
2
1.9. Results
23
4
1.10. Discussion Post Hoc
27
4
2. The FPU Research Program: Echoes on a String
31
20
2.1. The Threads of a Research Program
31
1
2.2. The Nonlinear Discrete Lattice
32
1
2.3. Ford, 1961
33
4
2.4. Jackson, 1963
37
4
2.5. Ford and Waters, 1963
41
2
2.6. The Continuous String
43
2
2.7. In the Continuous Limit
45
1
2.8. Discreteness as Viscosity
46
1
2.9. The First Soliton Paper
47
4
3. The Kolmogorov-Arnold-Moser Theorem: "Here Comes the Surprise"
51
32
3.1. A Brief History of Dynamics
51
2
3.2. The Fundamental Problem of Dynamics
53
4
3.3. The Small Divisors Problem
57
3
3.4. Poincare to Kolmogorov
60
4
3.5. The Conjecture
64
2
3.6. Beyond the Blaze
66
6
3.7. The Henon and Heiles Simulation, 1964
72
11
4. Research Threads Come Together: Harmonic Convergence
83
20
4.1. The Story Continues
83
1
4.2. Izrailev and Chirikov, 1966
84
5
4.3. Zabusky and Deem, 1967
89
2
4.4. Walker and Ford, 1969: Physical Review
91
2
4.5. Ford and Lunsford, 1970
93
4
4.6. Lunsford and Ford, 1972
97
2
4.7. The Toda Lattice Is Integrable
99
4
Part II: Philosophy
103
36
5. Steps to an Epistemology of Simulation
105
34
5.1. Introduction
105
2
5.2. Hierarchy of Modeling
107
3
5.3. Historical Significance
110
1
5.4. Experiment
111
2
5.5. Epistemology
113
4
5.6. Preconceptions
117
5
5.7. Strategies for Belief and Pursuit
122
3
5.8. Case Study I: Fermi-Pasta-Ulam
125
3
5.9. Case Study II: Henon and Heiles
128
1
5.10. Methodology
129
3
5.11. Irreversibility
132
1
5.12. Proof
133
3
5.13. Proof and Simulation
136
3
Appendix A. Hamiltonian Dynamics: Language of Abstraction
139
16
A.1. Topology and Phase-Space Trajectories
140
1
A.2. Canonical Transformations
141
1
A.3. Transforming the Unperturbed String
141
1
A.4. Cyclic Coordinates
142
1
A.5. Liouville Integrability
143
1
A.6. The Action-Angle Variables
143
4
A.7. Dynamics on a Torus
147
1
A.8. Commensurability: Two Types of Motion
148
4
A.9. Digital Representation
152
1
A.10. Physical Reality and the Continuum
152
1
A.11. Perturbing the String
153
2
Glossary
155
2
References
157
10
Index
167