Heteroclinic bifurcations in damped rigid block motion

It is shown that heteroclinic bifurcations are present in a piecewise-linear system of ordinary differential equations that describe the rocking motion of a slender rigid block with damping. An exact expression is given for the bifurcation amplitude. Stable and unstable manifolds are analytically extended to explicitly reveal the intersections. As the damping increases, these bifurcations occur only at increasingly large forcing amplitudes, as manifolds move further apart. No perturbation methods are used in this analysis.