| 广义Birkhoff系统与一类组合梯度系统 |
| |
| 引用本文： | 梅凤翔,吴惠彬.广义Birkhoff系统与一类组合梯度系统[J].物理学报,2015,64(18):184501-184501. |
| |
| 作者姓名： | 梅凤翔 吴惠彬 |
| |
| 作者单位： | 1. 北京理工大学宇航学院, 北京 100081;2. 北京理工大学数学学院, 北京 100081 |
| |
| 基金项目： | 国家自然科学基金(批准号: 10932002, 11272050)资助的课题. |
| |
| 摘 要： | 提出一类组合梯度系统, 即将梯度系统与斜梯度系统相加而组成的一个系统, 并研究组合梯度系统的重要性质. 将广义Birkhoff系统在一定条件下化成组合梯度系统, 并利用组合梯度系统的性质来研究广义Birkhoff系统的积分和稳定性.
|
| 关 键 词： | 广义Birkhoff系统 组合梯度系统 积分 稳定性 |
| 收稿时间： | 2015-02-24 |
Generalized Birkhoff system and a kind of combined gradient system |
| |
| Mei Feng-Xiang,Wu Hui-Bin.Generalized Birkhoff system and a kind of combined gradient system[J].Acta Physica Sinica,2015,64(18):184501-184501. |
| |
| Authors: | Mei Feng-Xiang Wu Hui-Bin |
| |
| Institution: | 1. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China;2. School of Mathematics, Beijing Institute of Technology, Beijing 100081, China |
| |
| Abstract: | A combined gradient system which is obtained by adding a gradient system to a skew-gradient system is proposed. The property of the system is studied. Three results on its solution are obtained. Moreover, a criterion on the stability of the system is presented. The generalized Birkhoff system is a more extensive constrained mechanical system than Lagrange system, Hamilton system and Birkhoff system. The conditions under which a generalized Birkhoff system can be considered as a combined gradient system are given. When a generalized Birkhoff system is transformed into a combined gradient system, its integration and stability can be discussed by using the property. Finally, some examples are given to illustrate the application of our results. |
| |
| Keywords: | generalized Birkhoff system combined gradient system integration stability |
|
| 点击此处可从《物理学报》浏览原始摘要信息 |
| 点击此处可从《物理学报》下载免费的PDF全文 |
