  This paper concerns the small-time stabilization of some classes of
mechanical systems which are not stabilizable by means of at least continuous
state feedback laws. This is the case of nonholonomic mechanical systems, an
example being the unicycle robot, or for underactuated mechanical systems, an
example being the slider. Explicit time-varying feedback laws leading to
small-time stabilization are constructed for these two control systems. The
main tools are homogeneity, backstepping, and desingularization technics.
