On random rotations

A body receives a sequence of rotations through a fixed angle about an axis whose direction is arbitrary. The probability distribution governing the resulting orientation of the body is determined. The problem is generalized to the case where the axis of each individual rotation makes the same angle, Θ, with an axis fixed in the body but is otherwise random. The resulting distribution is shown, in the case , to reduce to the Roberts-Ursell distribution for random walk on a sphere. Some diffusion limits are examined.