  The problem of transient hysteresis cycles induced by the pre-sliding kinetic
friction is relevant for analyzing the system dynamics e.g. of micro- and
nano-positioning instruments and devices and their controlled operation. The
associated energy dissipation and consequent convergence of the state
trajectories occur due to the structural hysteresis damping of contact surface
asperities during reversals, and it is neither exponential (i.e. viscous type)
nor finite-time (i.e. Coulomb type). In this paper, we discuss the energy
dissipation and convergence during the pre-sliding cycles and show how a
piecewise smooth force-displacement hysteresis map enters into the energy
balance of an unforced system of the second order. An existing friction
modeling approach with a low number of the free parameters, the Dahl model, is
then exemplified alongside the developed analysis.
