BIFURCATION AND CHAOS ANALYSIS IN THE FURUTA PENDULUM
DING Yu-mei1,2;ZHANG Qi-chang1
(1.School of Mechanical Engineering, Tianjin University, Tianjin, 300072, China, 2.Scool of Science, Tianjin University of Science and Technology, Tianjin 300222 China)
Abstract： Study Hopf bifurcations by normal form theory and the Hopf thory in the Furuta pendulum system. We calculate the normal forms of the Hopf bifurcation systems. The stability of the limit cycle is discussed.The space trajectory are investigated via numerical simulation, which are aslo verified the validity of our analysis. Based on the Silnikov criterion, the chaotic characters of the dynamical systems are discussed. Using Cardano formula and series solution of differential equation, eigenvalue problem and the existence of homoclinic orbit are studied respectively. Furthermore, a rigorous proof for the existence of Silnikov-sense Smale horseshoes chaos is presented and some conditions which lead to the chaos are obtained.
2010, Vol. 29 
