Double impact periodic orbits for an inverted pendulum

作者：Shen Jun; Du Zhengdong^*

来源：International Journal of Non-Linear Mechanics, 2011, 46(9): 1177-1190.

DOI：10.1016/j.ijnonlinmec.2011.05.010

• Impact inverted pendulum
• Double impact periodic orbit
• Grazing bifurcation
• Piecewise linear system
• Chaos

There exist many types of possible periodic orbits that impact at the walls for the inverted pendulum impacting between two rigid walls. Previous studies only focused on single impact periodic orbits and symmetric periodic orbits that bounce back and forth between the two walls. They respectively correspond to Types I and II orbits in the Chow, Shaw and Rand classification. In this paper we discuss two types of double impact periodic orbits that have not been studied before. The equations need to be solved for double impact orbits are transcendental and it is very hard to see the structure of the solutions. Consequently the analysis of double impact orbits is much more difficult than that of Types! and II orbits. A combination of analytical and numerical methods is employed to investigate the existence, stability and bifurcations of these orbits. Grazing bifurcations, which do not present for Types I and II orbits, are also observed.

• 出版日期2011-11
• 单位四川大学