Based on a successful text, this second edition presents different concepts from dynamical systems theory and nonlinear dynamics. The introductory text systematically introduces models and techniques and states the relevant ranges of validity and applicability. New to this edition: 3 new chapters dedicated to Maps, Bifurcations of Continuous Systems, and Retarded Systems Key features: Retarded Systems has become a topic of major importance in several applications, in mechanics and other areas Provides a clear operational framework for conscious use of concepts and tools Presents a rich variety of examples, including their final outcome For most of the examples, the results obtained with the method of normal forms are equivalent to those obtained with other perturbation methods, such as the method of multiple scales and the method of averaging Explains and compares different applications of the considered concepts and techniques Assumes knowledge of basic calculus as well as the elementary properties of ordinary-differential equations

Ali Hasan Nayfeh received his B.S. in engineering science and his M.S. and Ph.D. in aeronautics and astronautics from Stanford University. He established and served as Dean of the College of Engineering, Yarmouk University, Jordan from 1980 to 1984. He is currently University Distinguished Professor of Engineering, Emeritus at the Virginia Polytechnic Institute and State University. He is the Founder and Editor-in-Chief of Nonlinear Dynamics and the Journal of Vibration and Control. Professor Nayfeh is a Fellow of the American Physical Society (APS), the American Institute of Aeronautics and Astronautics (AIAA), the American Society of Mechanical Engineers (ASME), the Society of Design and Process Science, and the American Academy of Mechanics (AAM).

Preface	p. xi
Introduction	p. 1
SDOF Autonomous Systems	p. 7
Introduction	p. 7
Duffing Equation	p. 9
Rayleigh Equation	p. 13
Duffing-Rayleigh-van der Pol Equation	p. 15
An Oscillator with Quadratic and Cubic Nonlinearities	p. 17
Successive Transformations	p. 17
The Method of Multiple Scales	p. 19
A Single Transformation	p. 21
A General System with Quadratic and Cubic Nonlinearities	p. 22
The van der Pol Oscillator	p. 24
The Method of Normal Forms	p. 25
The Method of Multiple Scales	p. 26
Exercises	p. 27
Systems of First-Order Equations	p. 31
Introduction	p. 31
A Two-Dimensional System with Diagonal Linear Part	p. 34
A Two-Dimensional System with a Nonsemisimple Linear Form	p. 39
An n-Dimensional System with Diagonal Linear Part	p. 40
A Two-Dimensional System with Purely Imaginary Eigenvalues	p. 42
The Method of Normal Forms	p. 43
The Method of Multiple Scales	p. 47
A Two-Dimensional System with Zero Eigenvalues	p. 48
A Three-Dimensional System with Zero and Two Purely Imaginary Eigenvalues	p. 52
The Mathieu Equation	p. 54
Exercises	p. 57
Maps	p. 61
Linear Maps	p. 61
Case of Distinct Eigenvalues	p. 62
Case of Repeated Eigenvalues	p. 64
Nonlinear Maps	p. 66
Center-Manifold Reduction	p. 72
Local Bifurcations	p. 76
Fold or Tangent or Saddle-Node Bifurcation	p. 76
Transcritical Bifurcation	p. 79
Pitchfork Bifurcation	p. 80
Flip or Period-Doubling Bifurcation	p. 81
Hopf or Neimark-Sacker Bifurcation	p. 85
Exercises	p. 91
Bifurcations of Continuous Systems	p. 97
Linear Systems	p. 97
Case of Distinct Eigenvalues	p. 98
Case of Repeated Eigenvalues	p. 99
Fixed Points of Nonlinear Systems	p. 100
Stability of Fixed Points	p. 100
Classification of Fixed Points	p. 101
Hartman-Grobman and Shoshitaishvili Theorems	p. 102
Center-Manifold Reduction	p. 103
Local Bifurcations of Fixed Points	p. 107
Saddle-Node Bifurcation	p. 108
Nonbifurcation Point	p. 110
Transcritical Bifurcation	p. 111
Pitchfork Bifurcation	p. 113
Hopf Bifurcation	p. 114
Normal Forms of Static Bifurcations	p. 117
The Method of Multiple Scales	p. 117
Center-Manifold Reduction	p. 126
A Projection Method	p. 132
Normal Form of Hopf Bifurcation	p. 137
The Method of Multiple Scales	p. 138
Center-Manifold Reduction	p. 141
Projection Method	p. 144
Exercises	p. 146
Forced Oscillations of the Duffing Oscillator	p. 161
Primary Resonance	p. 161
Subharmonic Resonance of Order One-Third	p. 164
Superharmonic Resonance of Order Three	p. 167
An Alternate Approach	p. 169
Subharmonic Case	p. 171
Superharmonic Case	p. 172
Exercises	p. 172
Forced Oscillations of SDOF Systems	p. 175
Introduction	p. 175
Primary Resonance	p. 176
Subharmonic Resonance of Order One-Half	p. 178
Superharmonic Resonance of Order Two	p. 180
Subharmonic Resonance of Order One-Third	p. 182
Parametrically Excited Systems	p. 187
The Mathieu Equation	p. 187
Fundamental Parametric Resonance	p. 188
Principal Parametric Resonance	p. 190
Multiple-Degree-of-Freedom Systems	p. 191
The Case of ¿ Near ¿₂ + ¿₁	p. 194
The Case of ¿ Near ¿₂ -¿₁	p. 194
The Case of ¿ Near ¿₂ + ¿₁ and ¿₃ - ¿₂	p. 194
The Case of ¿ Near 2¿₃ and ¿₂ + ¿₁	p. 195
Linear Systems Having Repeated Frequencies	p. 195
The Case of ¿ Near 2¿₁	p. 198
The Case of ¿ Near ¿₃ + ¿₁	p. 199
The Case of ¿ Near ¿₃ - ¿₁	p. 200
The Case of ¿ Near ¿₁	p. 200
Gyroscopic Systems	p. 205
The Case of ¿ Near 2¿₁	p. 208
The Case of ¿ Near ¿₂ - ¿₁	p. 208
A Nonlinear Single-Degree-of-Freedom System	p. 208
The Case of ¿ Away from 2¿	p. 209
The Case of ¿ Near 2¿	p. 211
Exercises	p. 212
MDOF Systems with Quadratic Nonlinearities	p. 217
Nongyroscopic Systems	p. 217
Two-to-One Autoparametric Resvnance	p. 220
Combination Autoparametric Resonance	p. 222
Simultaneous Two-to-One Autoparametric Resonances	p. 223
Primary Resonances	p. 223
Gyroscopic Systems	p. 225
Primary Resonances	p. 226
Secondary Resonances	p. 227
Two Linearly Coupled Oscillators	p. 229
Exercises	p. 232
TDOF Systems with Cubic Nonlinearities	p. 235
Nongyroscopic Systems	p. 235
The Case of No Internal Resonances	p. 236
Three-to-One Autoparametric Resonance	p. 238
One-to-One Internal Resonance	p. 239
Primary Resonances	p. 239
A Nonsemisimple One-to-One Internal Resonance	p. 240
A Parametrically Excited System with a Nonsemisimple Linear Structure	p. 244
Gyroscopic Systems	p. 249
Primary Resonances	p. 250
Secondary Resonances in the Absence of Internal Resonances	p. 251
Three-to-One Internal Resonance	p. 255
Systems with Quadratic and Cubic Nonlinearities	p. 257
Introduction	p. 257
The Case of No Internal Resonance	p. 262
The Case of Three-to-One Internal Resonance	p. 263
The Case of One-to-One Internal Resonance	p. 264
The Case of Two-to-One Internal Resonance	p. 266
Method of Multiple Scales	p. 267
Second-Order Form	p. 268
State-Space Form	p. 271
Complex-Valued Form	p. 274
Generalized Method of Averaging	p. 276
A Nonsemisimple One-to-One Internal Resonance	p. 279
The Method of Normal Forms	p. 279
The Method of Multiple Scales	p. 283
Exercises	p. 285
Retarded Systems	p. 287
A Scalar Equation	p. 287
The Method of Multiple Scales	p. 289
Center-Manifold Reduction	p. 291
A Single-Degree-of-Freedom System	p. 295
The Method of Multiple Scales	p. 296
Center-Manifold Reduction	p. 299
A Three-Dimensional System	p. 304
The Method of Multiple Scales	p. 306
Center-Manifold Reduction	p. 308
Crane Control with Time-Delayed Feedback	p. 311
Exercises	p. 313
References	p. 315
Further Reading	p. 319
Index	p. 325
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