InhaltsangabePreface ix 1 Introduction 1 1.1 Brief History 1 1.2 Book Layout 4 2 Nonlinear Dynamical Systems 7 2.1 Continuous Systems 7 2.2 Equilibriums and Stability 9 2.3 Bifurcation and Stability Switching 17 2.3.1 Stability and Switching 17 2.3.2 Bifurcations 26 3 An Analytical Method for Periodic Flows 33 3.1 Nonlinear Dynamical Systems 33 3.1.1 Autonomous Nonlinear Systems 33 3.1.2 NonAutonomous Nonlinear Systems 44 3.2 Nonlinear Vibration Systems 48 3.2.1 Free Vibration Systems 48 3.2.2 Periodically Excited Vibration Systems 61 3.3 TimeDelayed Nonlinear Systems 66 3.3.1 Autonomous Time-Delayed Nonlinear Systems 66 3.3.2 NonAutonomous TimeDelayed Nonlinear Systems 80 3.4 TimeDelayed, Nonlinear Vibration Systems 85 3.4.1 TimeDelayed, Free Vibration Systems 85 3.4.2 Periodically Excited Vibration Systems with Time-Delay 102 4 Analytical Periodic to Quasi-Periodic Flows 109 4.1 Nonlinear Dynamical Systems 109 4.2 Nonlinear Vibration Systems 124 4.3 TimeDelayed Nonlinear Systems 134 4.4 TimeDelayed, Nonlinear Vibration Systems 147 5 Quadratic Nonlinear Oscillators 161 5.1 Period1 Motions 161 5.1.1 Analytical Solutions 161 5.1.2 Frequency-Amplitude Characteristics 165 5.1.3 Numerical Illustrations 173 5.2 Periodm Motions 180 5.2.1 Analytical Solutions 180 5.2.2 Analytical Bifurcation Trees 184 5.2.3 Numerical Illustrations 206 5.3 Arbitrary Periodical Forcing 217 6 TimeDelayed Nonlinear Oscillators 219 6.1 Analytical Solutions 219 6.2 Analytical Bifurcation Trees 238 6.3 Illustrations of Periodic Motions 242 References 253 Index 257

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InhaltsangabePreface Chapter 1 Introduction 1 1.1 Brief history 1 1.2 boook layout 5 Chapter 2 Nonlinear Dynamical Systems 7 2.1 Continuous systems 7 2.2 Equilibrium and stability 10 2.3 Bifurcation and stability switching 20 2.3.1 Stability and switching 21 2.3.2 Bifurcations 32 Chapter 3 An Analytical Method for Periodic Flows 39 3.1 Nonlinear dynamical sysetms 39 3.1.1 Autonomous nonlinear systems 39 3.1.2 Nonautonomous nonlinear systems 51 3.2 Nonlinear vibration systems 55 3.2.1 Free vibration systems 56 3.2.2 Periodically excited vibration systems 70 3.3 Timedelayed nonlinear systems 75 3.3.1 Autonomous time-delayed nonlinear systems 75 3.3.2 Nonauthonomous, timedelayed nonlinear systems 95 3.4 Timedelayed nonlinear vibration systems 96 3.4.1 Timedelayed, free vibration systems 96 3.4.2 Periodically excited vibration systems with time-delay 114 Chapter 4 Analytical Periodic to Quasi-periodic Flows 121 4.1 Nonlinear dynamical sysetms 121 4.2 Nonlinear vibration systems 137 4.3 Timedelayed nonlinear systems 147 4.4 Timedelayed, nonlinear vibration systems 160 Chapter 5 Quadratic Nonlinear Oscillators 175 5.1 Period1 motions 175 5.1.1 Analytical solutions 175 5.1.2 Analytical predictions 180 5.1.3 Numerical illustrations 185 5.2 Periodm motions 191 5.2.1 Analytical solutions 196 5.2.2 Analytical bifurcation trees 200 5.2.3 Numiercal illustrations 185 5.3 Arbitrary periodic forcing 235 Chapter 6 Time-delayed Nonlinear Oscillators 237 6.1 Analytical solutions of period-m moitons 237 6.2 Analytical bifurcation trees 257 6.3 Illustrations of periodic motions 265 References 273 Subject index 277

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