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传递辛矩阵群收敛于辛Lie群

钟万勰 高强

钟万勰, 高强. 传递辛矩阵群收敛于辛Lie群[J]. 应用数学和力学, 2013, 34(6): 547-551. doi: 10.3879/j.issn.1000-0887.2013.06.001
引用本文: 钟万勰, 高强. 传递辛矩阵群收敛于辛Lie群[J]. 应用数学和力学, 2013, 34(6): 547-551. doi: 10.3879/j.issn.1000-0887.2013.06.001
ZHONG Wan-xie, GAO Qiang. Symplectic Group of the Transfer Matrix Converges to the Symplectic Lie Group[J]. Applied Mathematics and Mechanics, 2013, 34(6): 547-551. doi: 10.3879/j.issn.1000-0887.2013.06.001
Citation: ZHONG Wan-xie, GAO Qiang. Symplectic Group of the Transfer Matrix Converges to the Symplectic Lie Group[J]. Applied Mathematics and Mechanics, 2013, 34(6): 547-551. 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
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

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

  • 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.
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    [8] 钟万勰, 姚征. 时间有限元与保辛[J]. 机械强度, 2005, 27(2):178183.(ZHONG Wan-xie, YAO Zheng. Time domain FEM and symplectic conservation[J].Journal of Mechanical Strength ,2005, 27(2):178183.(in Chinese))
    [9] 钟万勰, 高强.约束动力系统的分析结构力学积分[J]. 动力学与控制, 2006, 4(3):193200.(ZHONG Wan-xie, GAO Qiang. Integration of constrained dynamical system via analytical structural mechanics[J]. Journal of Dynamics and Control, 2006, 4(3):193200.(in Chinese))
    [10] 钟万勰, 高强.辛破茧[M].大连:大连理工大学出版社, 2011.(ZHONG Wan-xie, GAO Qiang.Break the Limitation of Symplecticity[M]. Dalian: Dalian University of Technology Press, 2011.(in Chinese))
    [11] 钟万勰. 力、功、能量与辛数学[M]. 大连:大连理工大学出版社, 2007.(ZHONG Wan-xie.Force, Work, Energy and Sympletic Mathematics[M]. Dalian: Dalian University of Technology Press, 2007.(in Chinese))
    [12] Gao Q, Tan S J, Zhang H W, Zhong W X. Symplectic algorithms based on the principle of least action and generating functions[J].International Journal for Numerical Methods in Engineering, 2012, 89(4): 438508.
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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

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