On the dynamic properties of axially moving systems

The objective of the present paper is a deep analysis of some recent numerical and experimental results regarding the complex dynamics of axially moving systems. Such important mechanical systems exhibit interesting dynamic behaviors: homoclinic orbits; sub-harmonic responses; amplitude modulations; and chaos. These dynamics have been obtained numerically and in some cases have been experimentally observed. Using recent techniques of the non-linear time series analysis, the response of axially moving systems has been studied for a large variety of test cases. The correlation dimension of the time series, which is deeply related to the minimal dimension of a system able to reproduce the dynamics, is estimated. Lyapunov exponents are evaluated in order to quantify the response regularity. The present work gives a contribution towards understanding the complex dynamics observed both in conservative and dissipative systems. The dynamical phenomena are analyzed within the unified framework of the non-linear time series analysis. In the case of experimental data the new non-linear filtering techniques, based on the embedding techniques, have been applied to reduce high noise when classical techniques give bad results. (C) 2004 Elsevier Ltd. All rights reserved.