Furuta倒立摆的分岔与混沌动力学分析  

Bifurcation and chaos analysis of a furuta pendulum

作　　者：丁玉梅[1,2] 张琪昌[1] 

机构地区：[1]天津大学机械学院,天津300072 [2]天津科技大学理学院,天津300222

出　　处：《振动与冲击》2010年第2期21-25,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(项目编号:10872141);高等学校博士学科点专项科研基金资助课题(项目编号:20060056005);天津科技大学科学研究基金资助项目(项目编号:20070210)

摘　　要：利用Hopf定理和规范形理论,讨论了Furuta旋转倒立摆非线性数学模型的Hopf分岔特性。给出系统存在Hopf分岔的条件,讨论了周期轨道的稳定性,利用数值模拟,得到系统的相轨迹图,进一步验证分析过程的正确性。利用Silnikov定理,讨论了旋转倒立摆的混沌动力学特征。利用卡尔达诺公式和微分方程级数解讨论了该系统的特征值和同宿轨道的存在性,比较严格地证明了系统存在Smale马蹄意义下的混沌现象,并给出发生Silnikov型Smale混沌的条件。Hopf bifurcations in a Furuta pendulum system using normal form theory and Hopf thory were studied.The normal forms of the Hopf bifurcation system were computed.The stability of the limit cycle was discussed.The spacial trajectories were investigated via numerical simulation,they verified the validity of this analysis.Based on Silnikov criterion,the chaotic characters of the dynamic system were discussed.Using Cardano formula and the series solution of the differential equation,the eigenvalue problem and the existence of homoclinic orbit were studied,respectively.Furthermore,a rigorous proof for the existence of Silnikov-sense Smale horseshoe chaos was presented and some conditions leading to the chaos were obtained.

关 键 词：旋转倒立摆 HOPF分岔 同宿轨道 混沌系统 Silnikov定理 

分 类 号：O322[理学—一般力学与力学基础] O175[理学—力学]