Computational Methods for Nonlinear Dynamical Systems
Theory and Applications in Aerospace Engineering
- 1st Edition - September 28, 2022
- Latest edition
- Authors: Xuechuan Wang, Xiaokui Yue, Honghua Dai, Haoyang Feng, Satya N. Atluri
- Language: English
Computational Methods for Nonlinear Dynamical Systems: Theory and Applications in Aerospace Engineering proposes novel ideas and develops highly-efficient and accurate methods f… Read more
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Description
Description
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.
Key features
Key features
- 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
Readership
Readership
Senior undergraduates, postgraduates, researchers and engineers who are interested in nonlinear computational methods
Table of contents
Table of contents
Chapter 1 Introduction
1.1 The weighted residual methods
1.1.1 Problem description
1.1.2 Primal methods
1.1.3 Mixed methods
1.2 Application of weighted residual methods
1.2.1 Transient motions
1.2.2 Periodic motions
1.3 Finite difference methods
1.3.1 Explicit methods
1.3.2 Implicit methods
1.4 Asymptotic methods
1.4.1 Perturbation method
1.4.2 Adomian decomposition method
1.4.3 Picard iteration method
References
Chapter 2 Harmonic Balance Method and Time Domain Collocation Method
2.1 Collocation in a period of oscillation
2.2 Relationship between collocation and harmonic balance
2.2.1 Harmonic balance method
2.2.2 High dimensional harmonic balance method
2.2.3 Equivalence between HDHB and collocation
2.3 Initialization of Newton-Raphson method
2.3.1 Initial values for undamped system
2.3.2 Initial values for damped system
2.4 Numerical examples
2.4.1 Undamped Duffing equation
2.4.2 Damped Duffing equation
Appendix A:
Appendix B:
References
Chapter 3 Dealiasing for Harmonic Balance and Time Domain Collocation Methods
3.1 Governing equations of the airfoil model
3.2 Formulation of the HB method
3.2.1 Numerical approximation of Jacobian matrix
3.2.2 Explicit Jacobian matrix of HB
3.2.3 Mathematical aliasing of HB method
3.3 Formulation of the TDC method
3.3.1 Explicit Jacobian matrix of TDC
3.3.2 Mathematical aliasing of the TDC method
3.4 Numerical examples
3.4.1 RK4 results and spectral analysis
3.4.2 HBEJ vs. HBNJ
3.4.3 Aliasing analysis of the HB and TDC methods
3.4.4 Dealiasing via a marching procedure
Appendix
References
Chapter 4 Application of Time Domain Collocation in Formation Flying of Satellites
4.1 TDC searching scheme for periodic relative orbits
4.2 Initial values for TDC method
4.2.1 The C-W equations
4.2.2 The T-H equations
4.3 Evaluation of TDC search scheme
4.3.1 Projected closed orbit
4.3.2 Closed loop control
4.4 Numerical results
Appendix
References
Chapter 5 Local Variational Iteration Method
5.1 VIM and its relationship with PIM and ADM
5.1.1 VIM
5.1.2 Comparison of VIM with PIM and ADM
5.2 Local variational iteration method
5.2.1 Limitations of Global VIM
5.2.2 Variational homotopy method
5.2.3 Methodology of LVIM
5.3 Conclusion
References
Chapter 6 Collocation of Local Variational Iteration Method
6.1 Modifications of LVIM
6.1.1 Algorithm-1
6.1.2 Algorithm-2
6.1.3 Algorithm-3
6.2 Implementation of LVIM
6.2.1 Discretization using collocation
6.2.2 Collocation of algorithm-1
6.2.3 Collocation of algorithm-2
6.2.4 Collocation of algorithm-3
6.3 Numerical examples
6.3.1 The forced Duffing equation
6.3.2 The Lorenz system
6.3.3 The multiple coupled Duffing equations
6.4 Conclusion
References
Chapter 7 Application of Local Variational Iteration Method in Orbital Mechanics
7.1 LVIM and Quasi-Linearization Method
7.1.1 Local Variational Iteration Method
7.1.2 Quasi-Linearization method
7.2 Perturbed orbit propagation
7.2.1 Comparison of LVIM with MCPI
7.2.2 Comparison of LVIM with Runge-Kutta 12(10)
7.3 Perturbed Lambert’s problem
7.3.1 Using LVIM
7.3.2 Using Fish-Scale-Growing method
7.3.3 Using QLVIM
7.4 Conclusion
References
Chapter 8 Applications of Local Variational Iteration Method in Structural Dynamics
8.1 Elucidation of LVIM in structural dynamics
8.1.1 Formulae of LVIM
8.1.2 Large time interval collocation
8.1.3 LVIM algorithms for structural dynamical system
8.2 Mathematical model of a buckled beam
8.3 Nonlinear vibrations of a buckled beam
8.3.1 Bifurcations and chaos
8.3.2 Comparison between HHT and LVIM algorithms
8.4 Conclusion
Product details
Product details
- Edition: 1
- Latest edition
- Published: September 29, 2022
- Language: English
About the authors
About the authors
XW
Xuechuan Wang
XY
Xiaokui Yue
HD
Honghua Dai
HF
Haoyang Feng
SA