| 双摆内共振分岔分析 |
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| 引用本文： | 毕勤胜,陈予恕.双摆内共振分岔分析[J].应用数学和力学,2000,21(3):226-234. |
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| 作者姓名： | 毕勤胜 陈予恕 |
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| 作者单位： | 天津大学力学系, 天津 300072 |
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| 基金项目： | 国家自然科学基金资助（19990510） |
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| 摘 要： | 应用normal form理论,首先分析了复摆自治系统在1:1内共振临界点附近的Hopf分岔解及其在参数平面上的分岔转迁集的解析表达式,并与数值解进行了比较;然后,应用数值方法,得到了复摆非自治系统通向混沌的过程。
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| 关 键 词： | 内共振 Hopf分岔 转迁集 混沌 |
| 文章编号： | 1000-0887(2000)03-0226-09 |
| 收稿时间： | 1998-11-23 |
| 修稿时间： | 1998-11-23 |
Bifurcation Analysis of a Double Pendulum With Internal Resonance |
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| Bi Qinsheng,Chen Yushu.Bifurcation Analysis of a Double Pendulum With Internal Resonance[J].Applied Mathematics and Mechanics,2000,21(3):226-234. |
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| Authors: | Bi Qinsheng Chen Yushu |
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| Institution: | Department of Mechanics, Tianjin University, Tianjin 300072, P R China |
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| Abstract: | By employing the normal
form theory, the Hopf bifurcation and the transition boundary of an autonomous double
pendulum with 11 internal resonance at the critical point is studied. The results are
compared with numerical solutions. Further, by numerical methods, the road to chaos of a
non-autonomous system is presented in the end. |
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| Keywords: | internal resonance Hopf bifurcation transition boundary chaos |
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