- 非线性动力学系统的计算方法(航天工程理论及应用)(英文版)/西北工业大学精品学术著作
- - 作者：Xuechuan Wang//Xiaokue Yue//Honghua Dai//Haoyang Feng//Satya N.Atluri|责编:徐杨峰
  - 出版社：科学
  - ISBN：9787030739391
  - 出版日期：2023/06/01
  - 页数：230
- 售价：56

内容大纲
非线性动力学系统目前已经成为科学研究和工程应用的重点关注对象。由于缺乏齐次性和叠加性，非线性系统的解往往无法解析获得，只能求助于数值计算方法。然而，面对复杂的强非线性系统，传统数值方法在精度、效率、稳定性等方面常常受到限制，难以满足实际科研工作和工程任务中的仿真计算需求，亟需引入新的思路和方法，推动非线性系统解算的进一步发展。本书根据近十年来相关领域的部分研究成果和作者的研究工作，介绍了非线性动力学系统的一系列全局估计方法和局部计算方法。从经典的渐进方法、有限差分方法和加权残余法开始，对各类典型的非线性动力学系统计算方法进行梳理和总结。在理清已有方法发展脉络的同时，提出了一些新的计算方法研究思路，并借此导出了局部变分迭代法等一系列新型高性能计算方法。本书不仅从理论上对强非线性动力学系统的计算方法进行了归纳、总结和发展，也从具体的航空航天工程问题出发，对方法的实际应用进行了探讨。
本书可供航空航天相关领域科研工作者和工程技术人员阅渎，也可供航空航天相关专业的高等院校高年级本科生和研究生学习参考。
作者介绍
目录
Preface
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
2. Harmonic Balance Method and Time Domain Collocation Method
  2.1  Time 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 Dulling equation
    2.4.2  Damped Duffing equation
  Appendix A
  Appendix B
  References
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  Reconstruction harmonic balance method
  3.5  Numerical examples
    3.5.1  RK4 results and spectral analysis
    3.5.2  HBEJ vs. HBNJ
    3.5.3  Aliasing analysis of the HB and TDC methods
    3.5.4  Dealiasing via a marching procedure
  Appendix
  References
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
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
6. Collocation in Conjunction with the 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
7. Application of the Local Variational Iteration Method in Orbital Mechanics
  7.1  Local variational iteration method 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 local variational iteration method with the modified Chebyshev picard iteration method
    7.2.2  Comparison of FAPI with Runge-Kutta 12(10)
  7.3  Perturbed Lambert's problem
    7.3.1  Using FAPI
    7.3.2  Using the fish-scale-growing method
    7.3.3  Using quasilinearization and local variational iteration method
  7.4  Conclusion
  References
8. Applications of the Local Variational Iteration Method in Structural Dynamics

  8.1  Elucidation of LVIM in structural dynamics
    8.1.1  Formulas of the local variational iteration method
    8.1.2  Large time interval collocation
    8.1.3  LVlM 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
  Appendix A
  Appendix B
  Appendix C
  References
Index

内容大纲

作者介绍

目录

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