Chaotic responses of a harmonically excited spring pendulum moving in circular path

In this paper, the chaotic response of a harmonically excited spring pendulum that is moving in circular path is studied. This system is a nonlinear multi-degrees-of-freedom system and is a good example for several engineering applications such as ship motion. Using the multiple scales (MS) method [A. Nayfeh, Perturbation Methods, Wiley-Interscience, New York, 1973], the original non-autonomous system is reduced to a third-order approximate autonomous system. The approximate system is shown to have bifurcation leading to chaos.