The chaotic instability of a slowly spinning asymmetric top

G.H.M. van der Heijden & J.M.T. Thompson

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, chaos

To appear in Mathematical and Computer Modelling.