关键词: 倒摆, 线性稳定性, 平衡点, 分岔, 混沌

Abstract: An experimental device of the forced inverse pendulum is designed and the dynamical equation is proposed. By using the method of the linear stability analysis, the stability of the system is discussed in the neighborhood of the equilibrium points. The character of the solutions can be obtained by numerical simulation and other analysis methods. From the results of computer simulation and experiment some time-series diagrams, phase diagrams and bifurcation diagrams for the oscillations of this system, these show that there are various kind of dynamical phenomena in this simple system. Theory analysis and numerical simulation well agree with the experiment results.

Key words: inverse pendulum, equilibrium point, bifurcation, chaos