On Motion of Chaplygin Sleigh on a Horizontal Plane with Dry Friction

Abstract

This paper considers the motion problem of the Chaplygin sleigh, a rigid body resting on a horizontal plane and equipped with three legs, one of which ends with a semicircular blade orthogonal to the supporting plane. As in the Chaplygin problem, it is assumed that the blade cannot move perpendicularly to its plane but can slide without friction along the straight intersection between the blade plane and the reference plane and rotate around its vertical radius. In contrast to the Chaplygin problem, it is assumed that at other support points the body is affected by dry friction forces. The equations of motion of the system are derived and the body motion is qualitatively analyzed.