Equilibrium of a Solid Body Supported at One Point by a Rough Plane

Abstract

The problem of the possible and necessary (in the sense of Jellett) equilibrium of a solid body that is in contact at one of its points with a rough plane and is under the action of an arbitrary system of forces is considered. The mass distributions in the body (i.e., the central tensor of inertia and the position of the body center of mass relative to the supporting point) are assumed to be arbitrary. At the point of contact of the body with the support (unilateral constraint), a dry friction force acts obeying the classical Coulomb–Euler law. The necessary and sufficient conditions for obligatory equilibrium are obtained. These conditions are expressed by simple analytical formulas. A comparison is made with the corresponding results for the planar case obtained previously.