On the motion of a two-dimensional rigid body on a rough straight line

We study the motion (rolling motion) of a flat plate whose boundary is an arbitrary convex curve along a straight line. During the motion the plate is always in contact with the supporting line and subject to a dry friction. Plus, the plate is acted on by an arbitrary plane system of forces and at the point of contact only the unilateral constraint is assumed. All possible transitions from a rolling motion with slipping to a pure rolling without slipping and vice versa are classified. Necessary conditions for the plate to remain in contact with the line are obtained. The results obtained are used to study 1) the motion of a non-uniform circular disk, subject to gravity, on a rough horizontal straight line in the vertical plane and 2) the motion of a slender rod, subject to gravity, on a rough straight line.