Pose statistics for eccentric parts

In many contexts, it is very useful to have an estimate of the final orientation, or pose, of an object which is dropped onto a flat surface. In this paper, we consider the final orientation of an object which starts with a random orientation, and show how the shape of the object relates to the distribution of its final orientation. We define a notion of geometric eccentricity for d-dimensional objects, which takes into account both its shape and its center-of-mass. We show that under quasi-static conditions, the pose into which eccentric objects settle will be with high probability in a cluster of poses which are very close together. Furthermore, the probability of ending up in this range of poses increases, and the size of the range decreases, as the object gets more eccentric.