Calculation of Lyapunov exponents in systems with impacts

We apply a model based algorithm for the calculation of the spectrum of the Lyapunov exponents of attractors of mechanical systems with impacts. For that, we introduce the transcendental maps that describe solutions of integrable differential equations, between impacts, supplemented by transition conditions at the instants of impacts. We apply this procedure to an impact oscillator and to an impact-pair system (with periodic and chaotic driving). In order to show the method precision, for large parameters range, we calculate Lyapunov exponents to classify attractors observed in bifurcation diagrams. In addition, we characterize the system dynamics by the largest Lyapunov exponent diagram in the parameter space.