BIFURCATION AND CHAOS ANALYSIS IN THE FURUTA PENDULUM

DING Yu-mei;ZHANG Qi-chang

Journal of Vibration and Shock ›› 2010, Vol. 29 ›› Issue (2) : 21-25.

PDF(762 KB)
PDF(762 KB)
Journal of Vibration and Shock ›› 2010, Vol. 29 ›› Issue (2) : 21-25.
论文

BIFURCATION AND CHAOS ANALYSIS IN THE FURUTA PENDULUM

  • DING Yu-mei1,2;ZHANG Qi-chang1
Author information +
History +

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.

Key words

rotational inverted pendulum / Hopf Bifurcations / homoclinic orbit / chaotic system / Silnikov theorem

Cite this article

Download Citations
DING Yu-mei;ZHANG Qi-chang. BIFURCATION AND CHAOS ANALYSIS IN THE FURUTA PENDULUM[J]. Journal of Vibration and Shock, 2010, 29(2): 21-25
PDF(762 KB)

Accesses

Citation

Detail

Sections
Recommended

/