Braking of a Solid Body Supported by Two Supports on a Horizontal Rough Plane

Abstract

Dry friction between elements of mechanisms remains an important aspect of theoretical and applied problems of machine science. In many cases of mathematical modeling, to overcome the paradoxes associated with the application of the Coulomb law in describing the friction between the elements of mechanisms, it is necessary to take into account the flexibility of these elements. The problem of sliding a heavy body with two elastic support legs along a horizontal rough plane is considered. The support legs are massless rods that resting on the plane at one end. At the other end, the rods are connected to the body by means of viscoelastic springs. It is shown that with absolutely rigid fastening of the leg guides, it is impossible to balance the body when any type of asymmetry occurs. Sliding friction is described using the Coulomb law. Several different types of motion are found: sliding the legs in one direction, sliding the legs in different directions, sliding of one leg (rotation around a fixed point).