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.

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.

1. Introduction 2. Harmonic Balance Method and Time Domain Collocation Method 3. Dealiasing for Harmonic Balance and Time Domain Collocation Methods 4. Application of Time Domain Collocation in Formation Flying of Satellites 5. Local Variational Iteration Method 6. Collocation of Local Variational Iteration Method 7. Application of Local Variational Iteration Method in Orbital Mechanics 8. Applications of Local Variational Iteration Method in Structural Dynamics