Lagrange系统的广义斜梯度表示

详细信息    查看全文 | 推荐本文 |

英文篇名：GENERALIZED SKEW-GRADIENT REPRESENTATION FOR LAGRANGE SYSTEM 作者：楼智美 ; 王元斌 英文作者：Lou Zhimei;Wang Yuanbin;Department of Physics,Shaoxing University;Department of Mathematics,Shaoxing University; 关键词：Lagrange系统 ; 广义斜梯度系统 ; 稳定性 英文关键词：lagrange system;;generalized skew-gradient system;;stability 中文刊名：DLXK 英文刊名：Journal of Dynamics and Control 机构：绍兴文理学院物理系;绍兴文理学院数学系; 出版日期：2017-02-20 出版单位：动力学与控制学报 年：2017 期：v.15;No.58 基金：国家自然科学基金资助项目(11472177)~~ 语种：中文; 页：DLXK201701002 页数：4 CN：01 ISSN：43-1409/O3 分类号：8-11

摘要

提出广义斜梯度系统并研究其性质,给出非定常Lagrange系统成为广义斜梯度系统的条件,利用广义斜梯度系统的性质来研究力学系统的稳定性.举例说明结果的应用.
        A generalized skew-gradient system is proposed,and the characteristic of the system is also studied.Additionally,the condition under which a Lagrange system can be considered as a generalized skew-gradient system is obtained. It shows that the characteristic of the generalized skew-gradient system can be used to study the stability of the mechanics system. Moreover,some examples are given to illustrate the application of the results.

引文

1 Hirsch M W,Smale S,Devaney R L.Differential equations,dynamical systems and an introduction to chaos.Singapore:Elsevier,2008
    2 Mclachlan R I,Quispel G R W,Robidoux N.Geometric integration using discrete gradients.Philosophical Transactions of the Royal Society A,1999,357:1021~1045
    3 梅凤翔.关于梯度系统.力学与实践,2012,34(1):89~90 (Mei F X.On the gradient system.Mechanics in Engineering,2012,34(1):89~90(in Chinese))
    4 梅凤翔,吴惠彬.广义Birkhoff系统的梯度表示.动力学与控制学报,2012,10(4):289~292(Mei F X,Wu H B.A gradient representation of generalized Birkhoff system.Journal of Dynamics and Control,2012,10(4):289~292 (in Chinese))
    5 楼智美,梅凤翔.力学系统的二阶梯度表示.物理学报,2012,61(2):024502(Lou Z M,Mei F X.A second order gradient representation of mechanics system.Acta Physica Sinica,2012,61(2):024502(in Chinese))
    6 梅凤翔,崔金超,吴惠彬.Birkhoff系统的梯度表示和分数维梯度表示.北京理工大学学报,2012,32(12):1298~1300(Mei F X,Cui J C,Wu H B.A gradient representation and a fractional gradient representation of Birkhoff system.Journal of Beijing Institute of Technology,2012,32(12):1298~1300(in Chinese))
    7 梅凤翔.分析力学Ⅱ.北京:北京理工大学出版社,2013(Mei F X.2013 Analytical mechanicsⅡ.Beijing:Beijing Institute of Technology Press(in Chinese))
    8 葛伟宽,薛纭,楼智美.完整力学系统的广义梯度表示.物理学报,2014,63(11):110202(Ge W K,Xue Y,Lou Z M.Generalized gradient representation of holonomic mechanical systems.Acta Physica Sinica,2014,63(11):110202(in Chinese))
    9 梅凤翔,吴惠彬.事件空间中完整力学系统的梯度表示.物理学报,2015,64(23):234501(Mei F X,Wu H B.A gradient representation of holonomic system in the event space.Acta Physica Sinica,2015,64(23):234501(in Chinese))
    10 Mei F X,Wu H B.Skew-gradient representation of generalized Birkhoffian system.Chinese Physics B,2015,24(10):104502
    11 梅凤翔,吴惠彬.一阶Lagrange系统的梯度表示.物理学报,2013,62(21):214501(Mei F X,Wu H B.A gradient representation of first-order Lagrange system.Acta Physica Sinica,2013,62(21):214501(in Chinese))
    12 Mei F X,Cai J C.Skew-gradient representation of constrained mechanical systems.Applied Mathematics and Mechanics,2015,36(7):873~882