We prove that for any non-trivial perturbation depending on any two
independent harmonics of a pendulum and a rotor there is global instability.
The proof is based on the geometrical method and relies on the concrete
computation of several scattering maps. A complete description of the different
kinds of scattering maps taking place as well as the existence of piecewise
smooth global scattering maps is also provided.Comment: 23 pages, 14 figure