Computational Methods for Nonlinear Dynamical Systems

Computational Methods for Nonlinear Dynamical Systems: Theory and Applications in Aerospace Engineering proposes novel ideas and develops highly-efficient and accurate methods for solving nonlinear dynamic systems, drawing inspiration from the weighted residual method and the asymptotic method. Proposed methods can be used both for real-time simulation and the analysis of nonlinear dynamics in aerospace engineering. The book introduces global estimation methods and local computational methods for nonlinear dynamic systems. Starting from the classic asymptotic, finite difference and weighted residual methods, typical methods for solving nonlinear dynamic systems are considered.In addition, new high-performance methods are proposed, such as time-domain collocation and local variational iteration. The book summarizes and develops computational methods for strongly nonlinear dynamic systems and considers the practical application of the methods within aerospace engineering.
- Presents global methods for solving periodic nonlinear dynamical behaviors
- Gives local methods for solving transient nonlinear responses
- Outlines computational methods for linear, nonlinear, ordinary and partial differential equations
- Emphasizes the development of accurate and efficient numerical methods that can be used in real-world missions
- Reveals practical applications of methods through orbital mechanics and structural dynamics

Xuechuan Wang is an Associate Researcher at Northwestern Polytechnical University, China. His research has focused on the frontiers of space exploration, and specifically, on computational methods for nonlinear dynamical systems.Xiaokui Yue is a Professor at Northwestern Technical University, China. His research has focused on the frontiers of space exploration and on computational methods for nonlinear dynamical systems.Honghua Dai is a Professor at Northwestern Technical University, China. His research has focused on the frontiers of space exploration and, specifically, on computational methods for nonlinear dynamical systems.Haoyang Feng is a Doctoral Student at Northwestern Polytechnical University, China. He works on computational methods for nonlinear dynamical systems at Northwestern Polytechnical University, a leading institute at the frontier of space exploration.Presidential Chair & University Distinguished Professor of Texas Tech University, has a fellowship of the American Institute of Aeronautics & Astronautics, and academy membership of USA National Academy of Engineering.

1. Introduction2. Harmonic Balance Method and Time Domain Collocation Method3. Dealiasing for Harmonic Balance and Time Domain Collocation Methods4. Application of Time Domain Collocation in Formation Flying of Satellites5. Local Variational Iteration Method6. Collocation of Local Variational Iteration Method7. Application of Local Variational Iteration Method in Orbital Mechanics8. Applications of Local Variational Iteration Method in Structural Dynamics