Lyapunov's Exponents for nonsmooth Dynamics with Impacts: Stability Analysis of the Rocking Block

The plane dynamics of a rigid block simply supported on a harmonically moving rigid ground is a problem which still needs investigating, although the matter has been the subject of much research since the last century. Unilateral contacts, Coulomb friction and impacts make the system hybrid as it reveals a mixed continuous and discontinuous nature. Thus, stability analysis requires the extension and adaptation of concepts with regard to variational-perturbative procedures. In particular, discontinuous systems exhibit discontinuities or “saltations” in the fundamental solution matrix which must be analyzed carefully. In this paper, the adaptation of numerical methods that permit us to obtain characteristic multipliers and Lyapunov’s exponents for the rocking mode of the block will be tackled. Analytical methods are used for the linearized equations of motion; the results are compared with those in the scientific literature.