Toward analytical chaos in nonlinear systems
"Exact analytical solutions to periodic motions in nonlinear dynamical systems are almost not possible. Since the 18th century, one has extensively used techniques such as perturbation methods to obtain approximate analytical solutions of periodic motions in nonlinear systems. However, the pert...
| Otros Autores: | |
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Chichester, England :
Wiley
2014.
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| Edición: | 1st edition |
| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009628458206719 |
Tabla de Contenidos:
- Machine generated contents note: Preface 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 Non-autonomous 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 Time-delayed nonlinear systems 75 3.3.1 Autonomous time-delayed nonlinear systems 75 3.3.2 Non-authonomous, time-delayed nonlinear systems 95 3.4 Time-delayed nonlinear vibration systems 96 3.4.1 Time-delayed, 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 Time-delayed nonlinear systems 147 4.4 Time-delayed, nonlinear vibration systems 160 Chapter 5 Quadratic Nonlinear Oscillators 175 5.1 Period-1 motions 175 5.1.1 Analytical solutions 175 5.1.2 Analytical predictions 180 5.1.3 Numerical illustrations 185 5.2 Period-m 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 .
