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Acta Mathematicae Applicatae Sinica 2001年第4期17卷 475-483页

作者：程代展薛伟民廖立志蔡大用 Institute of System Sciences Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong China Department of Applied Mathematics Tsinghua University Beifing China

The purpose of this paper is to explore an extension of some fundamental properties of the Hamiltonian systems to a more general case. We first extend symplectic group to a general N- group, GN, and prove that it has certain similar properties. A particular property of GN is that as a Lie group dim (GN)≥1. Certain properties of its Lie-algebra 9N are investigated. The results obtained are used to investigate the structure-preserving systems, which generalize the property of symplectic form preserving of Hamiltonian system to a covariant tensor field preserving of certain dynamic systems. The results provide a theoretical benchmark of applying symplectic algorithm to a considerably larger class of structure-preserving systems.

关键词： Hamiltonian systems Hamiltonian control systems symplectic group symplectic algebra symplectic algorithm

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Numerical algorithms for Solving Restricted Three Body Problem

Numerical Algorithms for Solving Restricted Three Body Probl...

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World-Association-of-Science-Engineering Global Congress on Science Engineering (GCSE 2010)

作者： Zhang, Yunyan Li, Yanjun Li, Nan NW Polytech Univ Sch Astronaut Xian 710072 Peoples R China

ISBN: (纸本)9780878492121

A precise integration algorithm for solving the restricted three body problem was put forward based on precise integration method, which divided a large integration time into small intervals and only small value matrix participates in the iterative process during the computation of the exponent matrix. And another symplectic algorithm for solving non-separable Hamiltonian system constructed by flow complex was also introduced, which only had periodic variational energy. The results of both algorithms were compared with fourth Runge-Kutta algorithm and their performances and advantages were analyzed, showing the validities of these two algorithms.

关键词： precise integration symplectic algorithm Hamiltonian system restricted three body problem

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Nonlocal Analytical Formulas for Plane Crack Elements and Semi-Analytical Element Method for Mode I Crack

Nonlocal Analytical Formulas for Plane Crack Elements and Se...

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2nd International Conference on Advances in Computational Modeling and Simulation (ACMS 2013)

作者： Zheng, Changliang Yao, Zheng Dalian Maritime Univ Transportat Equipment & Ocean Engn Coll Dalian 116026 Liaoning Peoples R China

ISBN: (纸本)9783037859063

This paper presents the series solutions in Hamiltonian form for plane sectorial domain of the nonlocal linear elasticity originally proposed by Eringen [1]. Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques were employed to obtain these solutions. These solutions can be used to develop a nonlocal analytical finite element for the model I crack in nonlocal fracture mechanics.

关键词： Nonlocal mechanics Hamilton theory Variational principle symplectic algorithm Plane fracture

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Elastic wavefield modeling by the symplectic discrete singular convolution differentiator method

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Acta Geophysica Sinica 2012年第3期55卷 343-351页

作者： Li, Yi-Qiong Li, Xiao-Fan Zhang, Mei-Gen Institute of Geology and Geophysics Chinese Academy of Sciences Beijing 100029 China Institute of Geophysics China Earthquake Administration Beijing 100081 China

In this paper, we introduce a structure-preserving method based on the symplectic discrete singular convolution differentiator (SDSCD) for simulating elastic wave fields. In the method presented for solving elastic wave equations, physical space is discretized by the singular convolution differentiator, whereas a symplectic difference scheme is used for the time discretization. With this method, the computational accuracy and stability have been greatly improved compared with traditional pseudo-spectral method. Numerical results suggest the SDSCD algorithm can suppress effectively numerical dispersion, and is suitable for modeling the large-scale and long-duration seismic wave propagation.

关键词： Discrete singular convolution differentiator Elastic wave fields modeling symplectic algorithm

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DYNAMICS MODELING AND symplectic COMPUTATION OF THE ROTATING TAPER STRUCTURE IN THE FRAMEWORK OF HAMILTON

DYNAMICS MODELING AND SYMPLECTIC COMPUTATION OF THE ROTATING...

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The Second International Conference on Dynamics Vibration and Control

作者： Yongan Huang, Linxiao Yao and Zichen Deng Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, China State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, China

The dynamics model of a rotating taper flexible beam with tip mass is established in the framework of Hamilton by the Finite Element Method (FEM), and the 2nd-order half-implicit symplectic Runge-Kutta (SRK) algorithm is developed to solve the rigid-flexible coupled model, so that the stability of the numerical simulation can be kept in a long period of time. Firstly, the continuous model of the rotating rigid-flexible structure is deduced by generalized Hamilton principle, and its discrete model is

关键词： symplectic algorithm rigid-flexible coupled system hamilton system canonical equation

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Static/dynamic Analysis of Functionally Graded and Layered Magneto-electro-elastic Plate/pipe under Hamiltonian System

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Chinese Journal of Aeronautics 2008年第1期21卷 35-42页

作者：代海涛北京航空航天大学航空科学与工程学院

The 3-dimensional couple equations of magneto-electro-elastic structures are derived under Hamiltonian system based on the Hamilton principle. The problem of single sort of variables is converted into the problem of double sorts of variables, and the Hamilton canonical equations are established. The 3-dimensional problem of magneto-electro-elastic structure which is investigated in Euclidean space commonly is converted into symplectic system. At the same time the Lagrange system is converted into Hamiltonian system. As an example, the dynamic characteristics of the simply supported functionally graded magneto-electro-elastic material （FGMM） plate and pipe are investigated. Finally, the problem is solved by symplectic algorithm. The results show that the physical quantities of displacement, electric potential and magnetic potential etc. change continuously at the interfaces between layers under the transverse pressure while some other physical quantities such as the stress, electric and magnetic displacement are not continuous. The dynamic stiffness is increased by the piezoelectric effect while decreased by the piezomagnetic effect.

关键词： functionally graded magneto-electro-elastic material Hamiltonian system symplectic algorithm

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Large Deformation Dynamic Analysis of a Cable System by a New Hamiltonian Finite Element Method

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INTERNATIONAL JOURNAL OF APPLIED MECHANICS 2021年第6期13卷

作者： Ding, Huaiping Yin, Xiaochun Wang, Qiao Zhu, Zheng H. Nanjing Univ Sci & Technol Dept Mech & Engn Sci 200 Xiaolingwei St Nanjing 210094 Peoples R China Inner Mongolia North Heavy Ind Grp Co Ltd Inst Equipment Res 3 Binggong Rd Baotou 014030 Inner Mongolia Peoples R China York Univ Dept Mech Engn Toronto ON M3J 1P3 Canada

This paper develops a new Hamiltonian nodal position finite element method for dynamic analysis of spatial flexible cable systems with large deformation. The dynamic governing equation is derived from finite elasticity theory. Logarithmic strain is applied to construct large deformation Hamiltonian canonical equations. An efficient second-order symplectic difference algorithm is built to solve the canonical equations numerically. A large strain conical pendulum system is analyzed numerically by the proposed method, and the numerical results are compared with those retracted from the existing Hamiltonian methods and Livermore Software Technology Corporation: dynamics (LS-DYNA). The proposed method is further verified by two tethered dynamic experiments involving large displacement motion and large deformation. The comparisons and verifications demonstrate that the proposed method is of symplectic conservation, has high accuracy and has stability for calculating flexible cable system dynamics with large deformation.

关键词： Cable systems dynamics large deformation nodal position finite element method Hamiltonian symplectic algorithm

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Enhanced excitation and ionization of H2+ by a single- and two-color intense laser pulse

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Physical Review A 2008年第6期77卷 063415-063415页

作者： Xue-Bin Bian Liang-You Peng Ting-Yun Shi State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences Wuhan 430071 China Graduate School of the Chinese Academy of Sciences Beijing 100049 China State Key Laboratory for Mesoscopic Physics and Department of Physics Peking University Beijing 100871 China

We study the enhanced excitation and ionization of H2+ by a single- and a two-color intense laser pulse. Our results show that the enhanced ionization in a single-color laser field is closely related to the dominant population of the 1σg or 1σu state and the corresponding width of their Floquet complex quasienergies. The overall trend of the population in higher excited states, once populated, remains flat as a function of time. Therefore, in the single-color case, the excited states do not contribute directly to the ionization. However, when the H2+ is exposed to a two-color laser field, an enhanced excitation effect to higher excited states for H2+ at some critical internuclear distance Rc is observed, which contributes greatly to the enhanced ionization of H2+ because of their much higher ionization rates compared to those of 1σg or 1σu states. We also find that the enhanced ionization is sensitive to the relative phase of the two-color laser field. By adjusting the relative phase, one can manipulate the enhanced ionization to occur at some critical internuclear distances. This can help the molecule to survive the enhanced ionization peaks at smaller internuclear distances, which is very useful for those circumstances where the preparation of expanded molecules is needed, e.g., for a more efficient generation of high-order harmonic generation. Our method is based on a numerical solution of the full-dimensional time-dependent Schrödinger equation accurately using a method we recently developed.

关键词： INDEPENDENT SCHRODINGER-EQUATION symplectic algorithm MOLECULAR IONIZATION FIELDS DISSOCIATION DYNAMICS RATES IONS

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线性哈密尔顿系统的m次连续有限元法

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高等学校计算数学学报 2011年第4期33卷 295-311页

作者：汤琼陈传淼刘罗华曹红萍湖南工业大学理学院湖南师范大学数学与计算机科学学院上海工程技术大学管理学院

1引言哈密尔顿系统是一个重要的动力系统,因此如何正确计算哈密尔顿系统有着重要的意义.正确的计算方法离散后应该保持着问题原型的基本特征.其中辛性质和能量守恒是哈密尔顿系统的两个重要特征.冯康和他的研究小组提出了哈密尔顿系统... 详细信息

1引言哈密尔顿系统是一个重要的动力系统,因此如何正确计算哈密尔顿系统有着重要的意义.正确的计算方法离散后应该保持着问题原型的基本特征.其中辛性质和能量守恒是哈密尔顿系统的两个重要特征.冯康和他的研究小组提出了哈密尔顿系统辛几何算法,

关键词： Hamilton equation continuous finite element method symplectic algorithm energy conservation

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Study on the finite element method of Hamiltonian system with chaos

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INTERNATIONAL JOURNAL OF MODERN PHYSICS C 2020年第11期31卷

作者： Tang, Qiong Liu, YangFan Zheng, Yujun Xu, ChengJie Hunan Univ Technol Coll Sci Zhuzhou 412007 Hunan Peoples R China Cent South Univ Sch Mat Sci & Engn Changsha 410083 Hunan Peoples R China Hunan Univ Sci & Engn Coll Sci Yongzhou 425199 Hunan Peoples R China Hunan Univ Technol Coll Sci Zhuzhou 412007 Hunan Peoples R China

By comparing with symplectic different methods, the quadratic element is an approximately symplectic method which can keep high accuracy approximate of symplectic structure for Hamiltonian chaos, and it is also energy conservative when there have chaos phenomenon. We use the quadratic finite element method to solve the Henon-Heiles system, and this method was never used before. Combining with Poincare section, when we increase the energy of the systems, KAM tori are broken and the motion from regular to chaotic. Without chaos, three kinds of methods to calculate the Poincare section point numbers are the same, and the numbers are different with chaos. In long-term calculation, the finite element method can better keep dynamic characteristics of conservative system with chaotic motion.

关键词： Hamiltonian systems chaos finite element methods symplectic algorithm Poincare section

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