On the Dynamics of a Solid on an Absolutely Rough Plane

An attempt is made to find a theoretical basis for some dynamic effects discovered experimentally in one problem of solid body dynamics on a plane, namely, the problem of the motion of the "celtic stone" [1-4]. The main attention is given to oscillations of a solid close to the equilibrium position or steady rotation. The motion is assumed to occur without friction and the supporting plane is fixed. Small oscillations of the body are briefly considered in the neighborhood of its steady rotation about the vertical. An approximate system of equations is obtained which describes non-linear oscillations of the body in the vicinity of its equilibrium position on a plane and a complete analysis is given. The results of the investigation agree with experimental observations [1,3] of the changes in the direction of rotation the celtic stone about the vertical without any external action, and the origin of rotation in any direction due to oscillations about the horizontal axis.