Bifurcations in gyroscopic systems with an application to rotating shafts

In this paper we study discrete nonlinear gyroscopic systems which can be obtained either in the context of rigid-body motions or by applying the Galerkin approximation to continuous systems. The problem considered in this paper is motivated by the whirling motion of a rotating shaft which is a fundamental component of many mechanical systems. The aim of our work is to study the effects of small dissipative and symmetry-breaking perturbations on bifurcations in gyroscopic systems, when the unperturbed Hamiltonian system with symmetry exhibits either a double zero or one-to-one resonance instability. Dissipative and symmetry-breaking perturbations, arising from imperfections inherent in most practical mechanical systems, can give rise to both local and global bifurcations. The general theoretical results for the two-degree-of-freedom gyroscopic systems are finally applied to study the dynamics of a rotating shaft.