We study how a top spinning in an unstable upright state can fall down in a
near-homoclinic 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 manoeuvres of spinning
bodies by applying subtle control techniques.
keywords: asymmetric top, (n-pulse) homoclinic orbits, bifurcations, stability, chaosTo appear in Mathematical and Computer Modelling.