In Vol 7 No 2 of Parabola, the following problem was set: A chess king is placed at the south-west corner of a chessboard.
In Figure 1, there are four different surfaces: the sphere, the cylinder, the torus, and the Mobius strip. I expect you are familiar with the first two of these.
The system which we consider consists of a pendulum bob of mass $m$ connected by a rigid rod of negligible mass to the pivot. This system is illustrated in Figure 1.