An approximate solution of a 2D rigid body motion problem on a rough surface

We report a novel general method for constructing an approximate solution of the planar motion of solids with an axially symmetric mass distribution and normal stresses over the contact area on a rough horizontal surface. For a disk characterized by Galin distribution of contact stresses we obtain explicit dependence of the angular and sliding velocity of the body as a function of time. The relative errors of the method do not exceed 1,5–2 %. The simplicity and high accuracy of the method let us recommend its applications in the practice of engineering calculations.