  Hysteresis is a special type of behavior encountered in physical systems: in
a hysteretic system, when the input is periodic and varies slowly, the
steady-state part of the output-versus-input graph becomes a loop called
hysteresis loop. In the presence of perturbed inputs, this hysteresis loop
presents small lobes called minor loops that are located inside a larger curve
called major loop. The study of minor loops is being increasingly popular since
it leads to a quantification of the loss of energy. The aim of the present
paper is to give an explicit analytic expression of the minor loops of the
LuGre and the Dahl models of dynamic dry friction.

Dynamical Systems