Second-order approximation for chaotic responses of a harmonically excitedspring-pendulum system

The influence of a higher-order approximation on chaotic responses of a wea kly non-linear multi-degree-of-freedom system is investigated. The specific system examined is a harmonically excited spring-pendulum system, which is known to be a good model for a variety of engineering systems, including s hip motions. By the method of multiple scales the original system is reduce d to a second-order approximate system. The long-term behaviors of both sys tems are compared by examining the largest Lyapunov exponents, It is observ ed that the second-order approximation gives better qualitative agreement w ith the original system than the first-order approximation does. (C) 1999 E lsevier Science Ltd. All rights reserved.