切塔耶夫型非完整系统的广义梯度表示

陈向炜; 曹秋鹏; 梅凤翔

doi:10.6052/0459-1879-15-268

切塔耶夫型非完整系统的广义梯度表示

1.
商丘师范学院物理与电气信息学院, 商丘 476000
2. 苏州科技学院数理学院, 苏州 215009
3. 北京理工大学宇航学院, 北京 100081

基金项目: 国家自然科学基金资助项目(11372169,10932002,11272050).

详细信息

通讯作者:
陈向炜,教授,主要研究方向:分析力学.E-mail:hnchenxw@163.com

中图分类号: O316
计量
- 文章访问数: 1293
- HTML全文浏览量: 84
- PDF下载量: 568
出版历程
- 收稿日期: 2015-07-19
- 修回日期: 2016-01-03
- 刊出日期: 2016-05-17

GENERALIZED GRADIENT REPRESENTATION OF NONHOLONOMIC SYSTEM OF CHETAEV'S TYPE

1.
Department of Physics and Information Engineering, Shangqiu Normal University, Shangqiu 476000, China
2. School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China
3. School of Aerospace, Beijing Institute of Technology, Beijing 100081, China

摘要

摘要: 非定常非完整力学系统的稳定性研究是重要而又困难的问题,直接从微分方程出发来构造李雅普诺夫函数往往很难实现.本文给出了一种间接方法.提出了10类广义梯度系统的定义,并分别给出了10类广义梯度系统的微分方程.进一步研究一般切塔耶夫型非完整系统的广义梯度表示,给出该系统分别成为这10类广义梯度系统的条件,从而将切塔耶夫型非完整系统化成各类广义梯度系统.最后利用广义梯度系统的性质来研究切塔耶夫型非完整系统零解的稳定性.这种方法在直接构造李雅普诺夫函数发生困难时,显得更为有效.举例说明结果的应用.
- 非完整系统 /
- 广义梯度系统 /
- 稳定性
Abstract: It is an important and di cult problem to study the stability of the non-steady and nonholonomic mechanical systems, and it is di cult to construct the Lyapunov function directly from the di erential equation. This paper gives an indirect method. The ten kinds of generalized gradient systems are proposed and the di erential equations of the ten kinds of generalized gradient systems are given respectively. Furthermore, the generalized gradient representations of a nonholonomic system of Chetaev's type are studied. The condition under which a nonholonomic system can be considered as a generalized gradient system is obtained, so the nonholonomic system of Chetaev's type is transformed into each generalized gradient systems. The characteristic of the generalized gradient systems can be used to study the stability of the nonholonomic system. This method appears to be more e ective when it is di cult to construct the Lyapunov function directly. Some examples are given to illustrate the application of the result.
- nonholonomic system /
- generalized gradient system /
- stability

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参考文献(30)

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施引文献(15)

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6.	尹明旭，谢煜，陈向炜. Nielsen方程的广义梯度表示及其稳定性分析. 力学季刊. 2022(02): 340-354 . 百度学术
7.	王嘉航，鲍四元. 事件空间中Birkhoff系统的两类广义梯度表示. 华中师范大学学报(自然科学版). 2020(02): 174-177 . 百度学术
8.	章婷婷，张毅，张成璞，陈向炜. 判定定常Chetaev型非完整系统稳定性的三重组合梯度方法. 动力学与控制学报. 2019(04): 306-312 . 百度学术
9.	董孟峰，陈向炜. 判定广义Birkhoff系统稳定性的三重组合梯度方法. 力学季刊. 2019(03): 543-548 . 百度学术
10.	李彦敏，章婷婷，梅凤翔. 用具有负定矩阵的梯度系统构造稳定的变质量力学系统. 力学学报. 2018(01): 109-113 . 本站查看
11.	章婷婷，陈向炜. 判定非自治Birkhoff系统稳定性的广义组合梯度方法. 力学季刊. 2018(04): 771-777 . 百度学术
12.	陈向炜，张晔，梅凤翔. 用具有负定非对称矩阵的梯度系统构造稳定的广义Birkhoff系统. 力学学报. 2017(01): 149-153 . 本站查看