华东师范大学学报(自然科学版) ›› 2017, Vol. ›› Issue (3): 94-98.doi: 10.3969/j.issn.1000-5641.2017.03.010

• 物理学与电子学 • 上一篇    下一篇

自治Birkhoff系统的四类梯度表示

崔金超1, 廖翠萃1, 梅凤翔2   

  1. 1. 江南大学 理学院, 江苏 无锡 214122;
    2.北京理工大学 宇航学院, 北京 100081
  • 收稿日期:2016-04-19 出版日期:2017-05-25 发布日期:2017-05-18
  • 作者简介:崔金超,男,讲师,研究方向为约束力学系统的稳定性.E-mail:cjcwx@163.com
  • 基金资助:
    国家自然科学基金（11272050，11401259）；江南大学自主科研资助项目（JUSRP11530）

Four kinds of gradient representations of autonomous Birkhoffian systems

CUI Jin-chao1, LIAO Cui-cui1, MEI Feng-xiang2   

  1. 1. School of Science, Jiangnan University, Wuxi Jiangsu 214122, China;
    2. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
  • Received:2016-04-19 Online:2017-05-25 Published:2017-05-18

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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.

关键词: Birkhoff系统, 梯度系统, 积分, 稳定性

Abstract: In order to study the integration and the stability of autonomous Birkhoffian systems, we propose four kinds of gradient systems to represent the autonomous Birkhoffian systems. By analysing the relationship between the gradient systems and the Birkhoffian systems, we obtain the conditions that the Birkhoffian systems can be transformed into a kind of four gradient systems. Then, we use the properties of gradient system to investigate the problems of integration and stability of the Birkhoffian systems. Finally, we give some examples to illustrate the application of the theory.

Key words: Birkhoffian systems, gradient system, integration, stability

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