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基于哈密顿动力系统新变分原理的保辛算法之二:算法保辛性质证明 被引量：4

The symplectic algorithms for Hamiltonian dynamic systems based on a new variational principle part II:the proof of the symplecticity
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摘要 文献[1]给出了哈密顿系统的一个新的变分原理,并基于此变分原理,通过选择一个时间步长两端不同广义位移或广义动量为独立变量,给出了四种不同类型的求解哈密顿动力系统的数值方法。本文将分别证明这四类数值方法都是保辛的数值方法。 In Reference [1-] ,a new variational principle for the finite dimensional autonomous Hamiltonian systems was proposed. Based on this new variational principle and by taking generalized coordinates or momenta as independent variables at each end of the time step,four types of numerical algorithms were constructed. In this paper,the proof of symplectic property of the four of numerical algorithms is giveh.
作者 高强 彭海军 张洪武 钟万勰
机构地区 大连理工大学工业装备结构分析国家重点实验室
出处 《计算力学学报》 CAS CSCD 北大核心 2013年第4期468-472,共5页 Chinese Journal of Computational Mechanics
基金 国家自然科学基金(11272076 10721062) 973项目(2011CB711105 2010CB832704) 中央高校基本科研业务费专项基金(DUT13LK12)资助项目
关键词 保辛 哈密顿系统 变分原理 作用量 symplectic Hamiltonian system ~ variational principle action
分类号 O322 [理学—一般力学与力学基础]
  • 相关文献

参考文献9

  • 1高强,彭海军,张洪武,钟万勰.基于哈密顿动力系统新变分原理的保辛算法之一:变分原理和算法构造[J].计算力学学报,2013,30(4):461-467. 被引量：9
  • 2Arnold V I. Mathematical Methods of Classical Me- chanics [M]. New York: Springer-Verlag, 1989.
  • 3Goldstein H. Classical Mechanics (Second Edition) [M]. London: Addison-Wesley, 1980.
  • 4Marsden J E,Ratiu T. Introduction to Mechanics and Symmetry (Second Edition) [ M]. Berlin: Springer, 1999.
  • 5Feng K. Difference schemes for Hamiltonian formal- ism and symplectic geometry[J]. Journal of Compu- tational Mathematics, 1986,4(3) : 279-289.
  • 6Feng K. On difference schemes and symplectic geom- etry[A]. Proceedings o5 the 5th International Sympo- sium on Differential Geometry and Differential Equa- tions[C]. Beijing, 1984.
  • 7H airer E,Lubich C, Wanner G. Geometric Numerical Integration : Structure-Preserving Algorithm for Ordinary Differential Equations (Second Edition) [M]. New York : Springer, 2006.
  • 8Hairer E,Norsett S P, Wanner G. Solving Ordinary Differential Equations I-Nonsti f f Problems (Second Edition) [M]. Berlin: Springer, 1993.
  • 9Hairer E,Wanner G. Solving Ordinary Differential Equations Ⅱ-Stiff and Differential- Algebraic Problems ( Second Edition) [ M ]. Berlin: Springer, 1996.

二级参考文献21

  • 1Arnold V I. Mathematical Methods of Classical Me- chanics [M]. New York : Springer-Verlag, 1989.
  • 2Goldstein H. Classical Mechanics (Second Edition) [M]. London : Addison-Wesley, 1980.
  • 3Marsden J E,Ratiu T. Introduction to Mechanics and Symmetry (Second Edition ) [M]. Springer: Berlin, 1999.
  • 4Hairer E,Lubich C, Wanner G. Geometric Numerical Integration : Structure-Preserving Algorithm for Or- dinary Differential Equations ( Second Edition ) [M]. New York:Springer,2006.
  • 5Hairer E, Norsett S P, Wanner G. Solving Ordinary Differential Equations I-Nonsti f f Problems (Sec- ond Edition) [M]. Berlin: Springer, 1993.
  • 6Hairer E,Wanner G. Solving Ordinary Differential Equations II-Stiff and Differential- Algebraic Problems ( Second Edition ) [M]. Berlin: Springer, 1996.
  • 7Ruth R D. A canonical integration technique [J]. IEEE Transactions on Nuclear Science, 1983, NS-30 (4) : 2669-2671.
  • 8Feng K. On difference schemes and symplectic geom- etry[A]. Proceedings of the 5th International Sympo- sium on Differential Geometry and Differential Equa- tions[C]. Beijing, 1984.
  • 9Wcndlandt J M, Marsden J E. Mechanical integrators derived from a discrete variational principle[J]. Phy- sica D,1997,106(3-4) :223-246.
  • 10Kane C, Marsden J E, Ortiz M,et al. Variational inte- grators and the newmark algorithm for conservative and dissipative mechanical systems[J]. International Journal for Numerical Methods in Engineering, 2000,49(10) : 1295-1325.

共引文献8

同被引文献38

  • 1Arnold V I. Mathematical Methods of Classical Me- chanics [M]. New York : Springer-Verlag, 1989.
  • 2Goldstein H. Classical Mechanics (Second Edition) [M]. London : Addison-Wesley, 1980.
  • 3Marsden J E,Ratiu T. Introduction to Mechanics and Symmetry (Second Edition ) [M]. Springer: Berlin, 1999.
  • 4Hairer E,Lubich C, Wanner G. Geometric Numerical Integration : Structure-Preserving Algorithm for Or- dinary Differential Equations ( Second Edition ) [M]. New York:Springer,2006.
  • 5Hairer E, Norsett S P, Wanner G. Solving Ordinary Differential Equations I-Nonsti f f Problems (Sec- ond Edition) [M]. Berlin: Springer, 1993.
  • 6Hairer E,Wanner G. Solving Ordinary Differential Equations II-Stiff and Differential- Algebraic Problems ( Second Edition ) [M]. Berlin: Springer, 1996.
  • 7Ruth R D. A canonical integration technique [J]. IEEE Transactions on Nuclear Science, 1983, NS-30 (4) : 2669-2671.
  • 8Feng K. On difference schemes and symplectic geom- etry[A]. Proceedings of the 5th International Sympo- sium on Differential Geometry and Differential Equa- tions[C]. Beijing, 1984.
  • 9Wcndlandt J M, Marsden J E. Mechanical integrators derived from a discrete variational principle[J]. Phy- sica D,1997,106(3-4) :223-246.
  • 10Kane C, Marsden J E, Ortiz M,et al. Variational inte- grators and the newmark algorithm for conservative and dissipative mechanical systems[J]. International Journal for Numerical Methods in Engineering, 2000,49(10) : 1295-1325.

引证文献4

二级引证文献11

计算力学学报
2013年 第4期

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