The planar rocking of a prismatic rectangular rigid block about either
of its corners is considered. The problem of homoclinic intersections
of the stable and unstable manifolds of the perturbed separatrix is a
ddressed to and the corresponding Melnikov functions are derived. Incl
usion of the vertical forcing in the Hamiltonian permits the construct
ion of a three-dimensional separatrix. The corresponding modified Meln
ikov function of Wiggins for homoclinic intersections is derived. Furt
her, the 1-period symmetric orbits are predicted analytically using th
e method of averaging and compared with the simulation results. The st
ability boundary for such orbits is also established.