The classical method is related to the calculation of the Lyapunov characteristic exponents (LCEs). One of the most important problems of nonlinear dynamics is related to the development of methods concerning the identification of the dynamical modes of the corresponding systems. It has been shown that the method provides values of the whole Lyapunov exponents spectrum with high accuracy. Bifurcation diagrams and Lyapunov exponents graphs have been generated. The mechanical oscillator with impact has been simulated. Efficiency of the method is confirmed by a numerical experiment. The algorithm of Jacobi matrix estimation is elaborated and an example is given. The article provides a detailed description of the method accompanied by clear schemes. In such a manner, direct calculation of the Jacobi matrix can be avoided. Therefore, the Jacobi matrix of the map is estimated using small perturbations of the initial point. However, the explicit formula of the map is usually not known. By analysing the map instead of the full trajectory, problems with transition of perturbations through discontinuities can be avoided. In the presented method, LEs are obtained from a Poincaré map. This paper covers application of the novel method of Lyapunov exponents (LEs) spectrum estimation in non smooth mechanical systems.
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