Dr. Yu Guo worked at Midwestern State University Texas as an Associate Professor. He previously worked at Caterpillar Inc. as an engine structural and dynamics engineer. Dr. Guo conducts research focusing on nonlinear vibration and impact dynamics. He has published 18 peer-reviewed journal papers, more than 20 conference articles, 4 book chapters, and 2 monographs. He has also conducted many professional presentations or invited lectures all over the world.Professor Albert C.J. Luo has worked at Southern Illinois University Edwardsville. For over 30 years, Dr. Luo’s contributions to nonlinear dynamical systems and mechanics lie in (i) the local singularity theory for discontinuous dynamical systems; (ii) dynamical systems synchronization; (iii) analytical solutions of periodic and chaotic motions in nonlinear dynamical systems; (iv) the theory for stochastic and resonant layer in nonlinear Hamiltonian systems; and (v) the full nonlinear theory for a deformablebody. Such contributions have been scattered into 28 monographs and over 350 peer-reviewed journal and conference papers. Dr. Luo served as an editor for the Journal of Communications in Nonlinear Science and Numerical Simulation, and book series on Nonlinear Physical Science (HEP and Springer) and Nonlinear Systems and Complexity (Springer). Dr. Luo was an editorial member for IMeCh E Part K Journal of Multibody Dynamics and Journal of Vibration and Control and has also organized over 30 international symposiums and conferences on dynamics and control.

• Preface.- Introduction.- Chapter 1 - A Semi-Analytical Method.- Chapter 2 - Discretization of a Spring-Pendulum.- Chapter 3 - Formulation for Periodic motions.- Chapter 4 - Period 1 motions to chaos varying with harmonic frequency.- Chapter 5 - Period 1 motions to chaos varying with harmonic amplitude.- Chapter 6 - Higher-order periodic motions to chaos.- References.

Dr. Yu Guo worked at Midwestern State University Texas as an Associate Professor. He previously worked at Caterpillar Inc. as an engine structural and dynamics engineer. Dr. Guo conducts research focusing on nonlinear vibration and impact dynamics. He has published 18 peer-reviewed journal papers, more than 20 conference articles, 4 book chapters, and 2 monographs. He has also conducted many professional presentations or invited lectures all over the world.Professor Albert C.J. Luo has worked at Southern Illinois University Edwardsville. For over 30 years, Dr. Luo’s contributions to nonlinear dynamical systems and mechanics lie in (i) the local singularity theory for discontinuous dynamical systems; (ii) dynamical systems synchronization; (iii) analytical solutions of periodic and chaotic motions in nonlinear dynamical systems; (iv) the theory for stochastic and resonant layer in nonlinear Hamiltonian systems; and (v) the full nonlinear theory for a deformablebody. Such contributions have been scattered into 28 monographs and over 350 peer-reviewed journal and conference papers. Dr. Luo served as an editor for the Journal of Communications in Nonlinear Science and Numerical Simulation, and book series on Nonlinear Physical Science (HEP and Springer) and Nonlinear Systems and Complexity (Springer). Dr. Luo was an editorial member for IMeCh E Part K Journal of Multibody Dynamics and Journal of Vibration and Control and has also organized over 30 international symposiums and conferences on dynamics and control.

• Preface.- Introduction.- Chapter 1 - A Semi-Analytical Method.- Chapter 2 - Discretization of a Spring-Pendulum.- Chapter 3 - Formulation for Periodic motions.- Chapter 4 - Period 1 motions to chaos varying with harmonic frequency.- Chapter 5 - Period 1 motions to chaos varying with harmonic amplitude.- Chapter 6 - Higher-order periodic motions to chaos.- References.

Dr. Yu Guo worked at Midwestern State University Texas as an Associate Professor. He previously worked at Caterpillar Inc. as an engine structural and dynamics engineer. Dr. Guo conducts research focusing on nonlinear vibration and impact dynamics. He has published 18 peer-reviewed journal papers, more than 20 conference articles, 4 book chapters, and 2 monographs. He has also conducted many professional presentations or invited lectures all over the world.Professor Albert C.J. Luo has worked at Southern Illinois University Edwardsville. For over 30 years, Dr. Luo’s contributions to nonlinear dynamical systems and mechanics lie in (i) the local singularity theory for discontinuous dynamical systems; (ii) dynamical systems synchronization; (iii) analytical solutions of periodic and chaotic motions in nonlinear dynamical systems; (iv) the theory for stochastic and resonant layer in nonlinear Hamiltonian systems; and (v) the full nonlinear theory for a deformablebody. Such contributions have been scattered into 28 monographs and over 350 peer-reviewed journal and conference papers. Dr. Luo served as an editor for the Journal of Communications in Nonlinear Science and Numerical Simulation, and book series on Nonlinear Physical Science (HEP and Springer) and Nonlinear Systems and Complexity (Springer). Dr. Luo was an editorial member for IMeCh E Part K Journal of Multibody Dynamics and Journal of Vibration and Control and has also organized over 30 international symposiums and conferences on dynamics and control.

• Preface.- Introduction.- Chapter 1 - A Semi-Analytical Method.- Chapter 2 - Discretization of a Spring-Pendulum.- Chapter 3 - Formulation for Periodic motions.- Chapter 4 - Period 1 motions to chaos varying with harmonic frequency.- Chapter 5 - Period 1 motions to chaos varying with harmonic amplitude.- Chapter 6 - Higher-order periodic motions to chaos.- References.