The chaotic instability of a slowly spinning asymmetric top

We study how a top spinning in an unstable upright state can fall down in a nearhomoclinic fashion, i.e., by repeatedly falling down and coming up again. A symmetric top shows regular behaviour but an asymmetric top can behave chaotically with infinitely many homoclinic orbits available. These orbits could be utilised in toppling and recovery maneuvers of spinning bodies by applying subtle control techniques.