NONLINEAR DYNAMICS OF A RIGID BLOCK ON A RIGID BASE

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.