The Not-so-simple Pendulum: Balancing a Pencil on its Point

Abstract

Does quantum mechanics matter at everyday scales? We generally assume that its consequences are confined to microscopic scales. It would be very surprising if quantum effects were to be manifest in a macroscopic system. This has been claimed for the problem of balancing a pencil on its tip. The claim has also been disputed. We argue that the behaviour of a tipping pencil can be explained by the asymptotic properties of the complete elliptic function, and can be understood in purely classical terms.