Lyapunov exponents estimation for strongly nonlinear nonsmooth discontinuous vibroimpact system

Abstract

Lyapunov exponents are ones of the most important characteristics for the definition of the dynamical system state. Their estimation for nonsmooth discontinuous system that is vibroimpact system has got certain difficulties. We study their calculation by following the evolution of two nearby orbits in phase space and use three formulas for such estimation. We check this calculation for three different oscillatory regimes: periodic, quasi-periodic and chaotic. We also define the largest Lyapunov exponent by Benettin’s algorithm and compare obtained results.