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

The book Computational Methods for Nonlinear Dynamical Systems: Theory and Applications in Aerospace Engineering develops novel methods for solving nonlinear dynamic systems in aerospace engineering, drawing inspiration from the weighted residual method and asymptotic method. It introduces global estimation methods and local computational methods and considers the practical application of the methods.

Format: Paperback / softback
Length: 240 pages
Publication date: 30 September 2022
Publisher: Elsevier - Health Sciences Division

Computational Methods for Nonlinear Dynamical Systems: Theory and Applications in Aerospace Engineering presents groundbreaking concepts and develops highly efficient and accurate methodologies for solving nonlinear dynamic systems. Drawing inspiration from the weighted residual method and the asymptotic method, these proposed methods have wide applications in real-time simulation and the analysis of nonlinear dynamics in aerospace engineering. The book explores global estimation methods and local computational methods for nonlinear dynamic systems, starting from classical approaches such as asymptotic, finite difference, and weighted residual methods. Additionally, it introduces innovative high-performance methods, including time-domain collocation and local variational iteration. The book summarizes and develops computational methods for strongly nonlinear dynamic systems, considering their practical implementation within aerospace engineering.

Introduction:
Nonlinear dynamical systems are prevalent in aerospace engineering, encompassing a wide range of systems such as aircraft, spacecraft, and propulsion systems. These systems are characterized by their complex behavior, which makes it challenging to predict and control their motion accurately. Computational methods play a crucial role in addressing these challenges by providing efficient tools for solving nonlinear dynamic systems.

Weighted Residual Method:
The weighted residual method is a powerful tool for solving nonlinear dynamic systems. It involves constructing a residual function that captures the difference between the predicted and actual system behavior. The weights assigned to the residuals are determined based on their magnitude and significance, allowing for the identification of critical regions and the development of efficient optimization algorithms.

Asymptotic Method:
The asymptotic method is another approach used to solve nonlinear dynamic systems. It relies on the expansion of the solution in terms of a series of functions, which can be approximated using mathematical techniques such as Taylor's series. This method is particularly useful for systems with large time-scales or when the solution is complex.

Global Estimation Methods:
Global estimation methods are used to estimate the state of a nonlinear dynamic system at any given time. These methods rely on the use of sensors and actuators to collect data about the system, which is then used to estimate the system's state. Global estimation methods are particularly useful in real-time simulation, where accurate and timely predictions are critical.

Local Computational Methods:
Local computational methods are used to solve nonlinear dynamic systems in specific regions or subdomains of the system. These methods are based on the discretization of the system's equations and the use of numerical methods such as finite difference and finite element methods. Local computational methods are particularly useful for systems with complex geometries or when the solution is highly dependent on local variables.

High-Performance Methods:
In recent years, there has been a growing interest in developing high-performance methods for solving nonlinear dynamic systems. These methods aim to reduce the computational time required for solving the systems while maintaining accuracy. Some of the high-performance methods proposed include time-domain collocation and local variational iteration.

Practical Applications:
The proposed computational methods have wide applications in aerospace engineering. They can be used for real-time simulation of aircraft and spacecraft, as well as for the analysis of nonlinear dynamics in propulsion systems. By accurately predicting the behavior of these systems, aerospace engineers can improve the safety, reliability, and efficiency of aerospace vehicles.

Conclusion:
Computational Methods for Nonlinear Dynamical Systems: Theory and Applications in Aerospace Engineering provides a comprehensive overview of the state-of-the-art computational methods for solving nonlinear dynamic systems. By drawing inspiration from the weighted residual method and the asymptotic method, the proposed methods offer highly efficient and accurate solutions for a wide range of aerospace engineering applications. The book is an invaluable resource for researchers, practitioners, and students in the field of aerospace engineering.

Dimension: 235 x 191 (mm)
ISBN-13: 9780323991131