Mechanics of the golf lip out

Sometimes, when a golfer attempts to putt a golf ball, it appears to enter the hole, only to re-emerge almost immediately, having undergone an angle of turn around the hole rim that can exceed 180∘. We consider the problem from the point of view of mechanics. We show analytically that there are at least two distinct types of lip out: the rim lip out, where the centre of mass of the golf ball does not fall below the level of the green, and the hole lip out where it does. At the heart of both lip outs is a family of degenerate saddle equilibria of the dynamics on the rim (the golf balls of death). When perturbed one way, the golf ball executes a rim lip out. When perturbed another way, the golf ball enters the hole, only to re-emerge (provided it does not touch the base of the hole) if it is spinning about an axis perpendicular to the wall of the hole.