  We consider the familiar problem of a bump, or ruck, in a rug. Under lateral
compression, a rug bends out of the plane forming a ruck -- a localized region
in which it is no longer in contact with the floor. We show that when the
external force that created the ruck is removed, the ruck flattens out unless
the initial compression is greater than a critical value, which we determine.
We also study the inertial motion of a ruck that is generated when one end of
the rug is moved rapidly. We show that the equations of motion admit a
travelling ruck solution for which a linear combination of the tension and
kinetic energy is determined by the ruck size. We confirm these findings
experimentally. We end by discussing the potential implications of our work for
the analogous propagation of localized slip pulses in the sliding of two bodies
in contact.
