The method of Melnikov for perturbations of multi-degree-of-freedom Hamiltonian systems

We develop a Melnikov-type global perturbation technique for detecting the existence of transverse homoclinic orbits and occurrence of homoclinic bifurcations in periodic perturbations of multi-degree-of-freedom Hamiltonian systems. The unperturbed system is assumed to have a saddle-centre whose stable and unstable manifolds do nor coincide but intersect in a lower-dimensional manifold, and does not have to be completely integrable. Other Melnikov-type methods do not apply in this situation. We also apply our technique to a four-degree-of-freedom model of nonplanar vibrations of a forced, buckled beam.