The Behaviour of a Mass on a Vibrating Table

Abstract

Impact motions of a mass on a harmonically and vertically vibrating table are considered. So-called 1/n-periodic motions (one impact per n periods of the vibrating table. n : integer) are determined analytically and their stability is analyzed. At the boundaries of a stable region of a 1/n-periodic motion one of the characteristic roots is equal to +1 or -1. At the boundary where one root is +1, saddle-node bifurcation occurs, and at the boundary where one root is -1 period doubling bifurcation occurs. Chaotic behaviour can be seen after the period doubling bifurcations. The strange attractor of the chaotic behaviour and the invariant curves are obtained.