传递辛矩阵群收敛于辛Lie群

钟万勰; 高强

doi:10.3879/j.issn.1000-0887.2013.06.001

传递辛矩阵群收敛于辛Lie群

doi: 10.3879/j.issn.1000-0887.2013.06.001

钟万勰,
高强

大连理工大学工业装备结构分析国家重点实验室, 工程力学系,辽宁大连 116024

基金项目: 国家自然科学基金资助项目(11272076; 10721062)

详细信息

作者简介:
钟万勰(1934—)，男，浙江人，教授，中科院院士(E-mail：zwoffice@dlut.edu.cn)

中图分类号: O152.8
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- 被引次数: 0
出版历程
- 收稿日期: 2013-04-24
- 修回日期: 2013-05-09
- 刊出日期: 2013-06-15

Symplectic Group of the Transfer Matrix Converges to the Symplectic Lie Group

State Key Laboratory of Structural Analysis of Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian, Liaoning 116023, P.R.China

摘要

摘要: 通过作用量变分原理，给出了Hamilton正则方程离散积分的传递辛矩阵表示，利用Hamilton正则方程给出了其对应的Lie代数．说明了当时间区段长度趋近于0时，离散系统积分的传递辛矩阵群收敛于连续时间Hamilton系统微分方程分析积分得到的辛Lie群．
- 离散积分 /
- 传递辛矩阵 /
- Hamilton /
- 辛Lie群
Abstract: By using action variational principle, the transfer symplectic matrix for the discrete integral of the Hamiltonian canonical equation was given. Then the Lie algebra corresponding to the Hamiltonian canonical equation was given. When the time step tends to zero, that the symplectic group of the transfer matrix for discrete integrator converges to the symplectic Lie group of the continuoustime differential equation of the Hamiltonian system was proved.
- discrete integration /
- symplectic group of the transfer matrix /
- Hamilton /
- symplectic Lie group

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参考文献(12)

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