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 (Goyal, Ruina, Papadopoulos [1990]). 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 direction in load space where P is parallel to the generalized motion direction q. For most objects, if the radius of gyration is sufficiently larger than the radius of the contact region final motion is always pure rotation about the center of mass; if the mass distribution is sufficiently central the 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