Quantitative Study of Chaos in a Piecewise Linear Mechanical System

Abstract

This paper presents a simple piecewise linear, two-degrees of freedom, differential active damper mechanical system, derived from an analogy to an electrical circuit. Analytical solutions for the state trajectory of this system are derived and discussed. Three different methods of quantifying the complicated chaotic dynamic behavior of the system are compared on the basis of their accuracy in estimating the regions of chaotic behavior. The concept of mean correlation delay function (MCD) is introduced as a simple and efficient quantifier of chaotic motion in deterministic systems with known absence of stochastic inputs.