摘要
通过对一类复摆系统的建模,利用数值分析法,较为全面地论证了复摆系统通向混沌的倍周期道路、拟周期道路等复杂的混沌演化行为.用相图、庞加莱映射图和分岔图等方式揭示出了系统混沌运动的形式和参数.对该系统分岔与混沌行为的研究,为工程实际中相关机械系统和振动系统的混沌预测和控制具有指导意义,同时对这些系统的优化设计提供了理论依据.
In this paper, the dynamic behaviour and chaotic phenomena of a double pendulum system were explored through numerical simulations. Bifurcations and chaos of the double pendulum system with two concentrated masses were investigated. The routes from quasi-periodic, period-doubling impacts to chaos, respectively, were discussed by bifurcation diagram, phase portraits and Poincaré map. The obtained result can be used in chaos prediction and chaotic control. It was proved that the routes of the double pendulum system impacts to chaos are complicated. It was possible to optimize system parameter of practical system by investigation of bifurcation and chaos.
出处
《华中科技大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2007年第5期27-30,共4页
Journal of Huazhong University of Science and Technology(Natural Science Edition)
基金
国家自然科学基金资助项目(50475109)
甘肃省自然科学基金资助项目(3ZS042-B25-043)
兰州交通大学"青蓝"人才工程基金资助项目(QL-06-05A)
关键词
复摆
周期运动
分岔
混沌
double pendulum
periodic motion
bifurcation
chaos
