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Four kinds of gradient representations of autonomous Birkhoffian systems

Jin-chao CUI Cui-cui LIAO Feng-xiang MEI

崔金超, 廖翠萃, 梅凤翔. 自治Birkhoff系统的四类梯度表示[J]. 华东师范大学学报(自然科学版), 2017, (3): 94-98. doi: 10.3969/j.issn.1000-5641.2017.03.010
引用本文: 崔金超, 廖翠萃, 梅凤翔. 自治Birkhoff系统的四类梯度表示[J]. 华东师范大学学报(自然科学版), 2017, (3): 94-98. doi: 10.3969/j.issn.1000-5641.2017.03.010
CUI Jin-chao, LIAO Cui-cui, MEI Feng-xiang. Four kinds of gradient representations of autonomous Birkhoffian systems[J]. Journal of East China Normal University (Natural Sciences), 2017, (3): 94-98. doi: 10.3969/j.issn.1000-5641.2017.03.010
Citation: CUI Jin-chao, LIAO Cui-cui, MEI Feng-xiang. Four kinds of gradient representations of autonomous Birkhoffian systems[J]. Journal of East China Normal University (Natural Sciences), 2017, (3): 94-98. doi: 10.3969/j.issn.1000-5641.2017.03.010

自治Birkhoff系统的四类梯度表示

doi: 10.3969/j.issn.1000-5641.2017.03.010
基金项目: 国家自然科学基金(11272050, 11401259);江南大学自主科研资助项目(JUSRP11530)
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    作者简介:
  • 中图分类号: O316

Four kinds of gradient representations of autonomous Birkhoffian systems

  • 摘要: 提出四类梯度系统, 并研究自治Birkhoff系统的梯度表示.给出系统成为梯度表示和分数维梯度的条件, 利用梯度系统的性质来研究Birkhoff系统的积分和解的稳定性, 举例说明结果的应用.
  • [1] HIRSCH M W, SMALE S, DEVANEY R L. Differential Equations, Dynamical Systems, and an Introduction to Chaos[M]. 3rd ed. Waltham, Academic Press, 2012.
    [2] MCLACHLAN R I, QUISPEL G R W, ROBIDOUX N. Geometric integration using discrete gradients[J]. Philosophical Transactions of the Royal Society of London: Series A, 1999, 357: 1021-1045. doi:  10.1098/rsta.1999.0363
    [3] LOU Z M, MEI F X. A second order gradient representation of mechanics system[J]. Acta Physica Sinica, 2012, 61: 337-340.
    [4] MEI F X. On the gradient system[J]. Mechanics in Engineering, 2012, 34: 89-90.
    [5] MEI F X, WU H B. A gradient representation for generalized Birkhoffian system[J]. Dynamics and Control, 2012, 10: 289-292.
    [6] MEI F X, WU H B. Generalized Hamilton system and gradient system[J]. Science China Physics, Mechanics and Astronomy, 2013, 43: 538-540. doi:  10.1360/132012-719
    [7] MEI F X, CUI J C, WU H B. A gradient representation and a fractional gradient representation of Birkhoff system[J]. Transactions of Beijing Institute of Technology, 2012, 32: 1298-1300.
    [8] MEI F X. Analytical Mechanics Ⅱ[M]. Beijing: Beijing Institute of Technology Press, 2013.
    [9] GUO Y X, LIU C, LIU S X. Generalized Birkhoffian realization of nonholonomic systems [J]. Communications in Mathematics, 2010, 18: 21-35.
    [10] SANTILLI R M. Foundations of Theoretical Mechanics Ⅱ[M]. New York: Springer, 1983.
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  • 被引次数: 0
出版历程
  • 收稿日期:  2016-04-19
  • 刊出日期:  2017-05-25

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