  We introduce a new analytical method, which allows to find out chaotic
dynamics in non-smooth dynamical systems. A simple mechanical system consisting
of a mass and a dry friction element is considered as an example. The
corresponding mathematical model is represented. We show that the considered
dynamical system is a skew product over a piecewise smooth mapping of a segment
(a base map). For this base map we demonstrate there is a domain of parameters
where a robust chaotic dynamics can be observed. Namely, we prove existence of
an infinite set of periodic points of arbitrarily big period. Moreover, a
reduction of the considered map is semi-conjugated to a shift on the set of
one-sided infinite boolean sequences. Also, we find conditions, sufficient for
existence of a superstable periodic point of this map. The obtained result
partially solves a general problem: theoretical confirmation of chaotic and
periodic regimes numerically and experimentally observed for models of
percussion drilling.
