Exact normal forces and trajectories for a rotating tripod sliding on a smooth surface

We study the motion of a rotating tripod sliding over a smooth surface. The tripod is important and unique in that it is the only case where all aspects of the motion can be solved exactly. From the three constraint equations, we calculate the three normal forces and friction forces, which we then use to calculate the trajectory and other physical quantities of interest. We report novel results: the normal force has an interesting form when the sliding speed and the speed of rotation are almost equal; the tripod can execute serpentine trajectories; trajectories can have large lateral deflections; the translational kinetic energy can decrease and increase during a full rotation; the tripod can tip at a very late stage of its motion. The tripod trajectories are compared to trajectories of rotating, sliding cylinders that have continuous contact rings. We discuss significant implications of our results.