Chaos in a soda can: Non-periodic rocking of upright cylinders with sensitive dependence on initial conditions

It has been known for over a hundred years that all physically realizable motions of an ideal axisymmetric cylinder, rolling without slip on its flat circular bottom atop a flat horizontal surface, are periodic in the cylinder's angular rates and quasi-periodic overall. Here, we show that slight asymmetries in the cylinder, say the addition of an off-center point-mass, result in non-periodic motions with exponentially increasing sensitivity to initial conditions, making the dynamics chaotic.