SLENDER RIGID BLOCK MOTION

The long-established equations for the motion of a free-standing rigid block under periodic forcing have been studied numerically and analytically in detail by the writer in several papers since 1989, when chaos was first shown to be present in the simple system of piecewise linear equations. Other results include the presence of multiple solutions, symmetry-breaking bifurcations, and period-doubling cascades as well as exact analytic results for some stability boundaries. Experimental results have been explained, and excellent agreement found with the straightforward theory. Numerical calculations have been performed on the same problem by other authors. In this paper it is shown that their work can be explained and broadened by the theory of the writer. The opportunity is taken to present several new results, including forcing-amplitude frequency diagrams for a range of coefficients of restitution. Results missed by these authors are also given.