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1 Introduction 1.1 Analytical Methods 1.1.1 Traditional Methods 1.1.2 Generalized Harmonic Balance 1.2 Galloping Phenomena 1.2.1 A Brief History cf Galloping Modeling 1.2.2 Mathematical Modeling 1.2.3 Aerodynamic Force and Moment 1.3 Book Layout References 2 Nonlinear Dynamical Systems 2.1 Continuous Systems 2.2 Equilibriums and Stability 2.3 Bifurcation and Stability Switching 2.3.1 Stability and Switching 2.3.2 Bifurcations References 3 Analytical Methods 3.1 Periodic Motions 3.2 Quasiperiodic Motions References 4 A Quadratic Nonlinear Oscillator 4.1 Analytical Period-m Motions 4.2 Analytical Bifurcation Trees 4.3 Numerical Illustrations References 5 Two-Degree-of-Freedom Nonlinear Oscillators 5.1 Analytical Solution Formulation 5.2 Frequency-Amplitude Characteristics 5.3 Numerical Simulations References 6 Linear Cable Galloping 6.1 Analytical Period-1 Motions 6.2 Frequency-Amplitude Characteristics 6.3 Numerical Simulations and Comparisons References 7 Nonlinear Cable Galloping 7.1 Analytical Period-m Motions 7.2 Analytical Bifurcation Trees 7.3 Numerical Illustrations References Appendix A: Coefficients for Cable Galloping Index