Computational Methods for Nonlinear Dynamical Systems: Theory and Applications in Aerospace Engineering

Traditional numerical methods are often of limited accuracy, efficiency and stability for complex and strong nonlinear systems. There is a need for new ideas and methods for solving nonlinear systems in order to meet the simulation requirements of modern science and engineering. Computational Methods for Nonlinear Dynamical Systems presents a series of global estimation methods and local computational methods for nonlinear dynamic systems, based on the latest research in aligned fields and the authors' own research.Computational Methods for Nonlinear Dynamical Systems 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. The proposed methods can be used both for real-time simulation and for 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. New high-performance methods are proposed such as time-domain collocation and local variational iteration. This 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 and 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 the methods through orbital mechanics and structural dynamics