On the motion of free disc on the rough horisontal plane

We consider the problem of a disk sliding on a horizontal plane under the action of dry friction forces. The model is based on three hypotheses. The law of interaction of a small element of the disk’s surface with the plane is the Amonton–Coulomb law, the pressure distribution over the contact patch is a linear (generally speaking, time-dependent) function of Cartesian coordinates, the height of the disk is not high. The equations of motion possess a rich group of symmetry, which enables a detailed qualitative analysis of the problem.