Princeton University Press
Nonlinear Oscillations in Physical Systems
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About this book
This book offers a fundamental explanation of nonlinear oscillations in physical systems. Originally intended for electrical engineers, it remains an important reference for the increasing numbers of researchers studying nonlinear phenomena in physics, chemical engineering, biology, medicine, and other fields.
Originally published in 1986.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Topics
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Frontmatter
iii -
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Preface
vii -
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Contents
ix -
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Introduction
1 - Part I. Principal Methods of Nonlinear Analysis
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Chapter 1. Analytical Methods
11 -
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Chapter 2 Topological Methods and Graphical Solutions
33 -
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Chapter 3. Stability of Nonlinear Systems
69 - Part II. Forced Oscillations in Steady States
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Chapter 4. Stability of Periodic Oscillations in Second-order Systems
101 -
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Chapter 5. Harmonic Oscillations
114 -
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Chapter 6. Higher-harmonic Oscillations
128 -
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Chapter 7. Subharmonic Oscillations
142 - Part IV. Self-oscillatory Systems with External Force
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Chapter 12. Entrainment of Frequency
285 -
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Chapter 13. Almost Periodic Oscillations
309 -
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Appendix I: Expansions of the Mathieu Functions
339 -
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Appendix II: Unstable Solutions of Kill's Equation
341 -
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Appendix III: Unstable Solutions fox* the Extended Form of Kill's Equation
343 -
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Appendix IV: Stability Criterion Obtained by Using the Perturbation Method
349 -
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Appendix V: Remarks Concerning Integral Curves and Singular Points
353 -
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Appendix VI: Electronic Switch
359 -
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Problems
362 -
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Bibliography
378 -
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Index
385