PLANAR SLIDING WITH DRY FRICTION .2. DYNAMICS OF MOTION

Some problems in the dynamics of sliding of planar rigid bodies are treated by geometric methods based on the limit surface description of friction (S. Goyal, A. Ruina and J. Papadopoulos, Wear, 143 (1991) 307-330). The problems we consider, where the normal force is known a priori, have unique solutions although the friction force (and torque) may be a discontinuous function of the direction of motion. When a freely sliding object comes to rest it always does so with one of several definite ratios of translation to rotation. These special generalized velocity directions, termed eigen-directions, depend on the friction law used, the contact pressure distribution and the mass distribution. The eigen-directions correspond to local extrema of the generalized frictional load \P\ on the limit surface, i.e. to directions in load space where P is parallel to the generalized direction of motion q. For most objects, if the contact region is sufficiently smaller than the radius of gyration, final motion is always pure rotation about the center of mass; if the contact region is sufficiently spread out final motion is a pure translation. A simple model of a car with locked rear wheels shows the effect of speed and orientation on skid stability at finite speeds. Sliders have a propensity to rotate about points of support.