Nonlinear oscillations of a suspended gyrostat

Abstract

In this paper, the nonlinear dynamics of the disturbed Hamiltonian systems of a suspended gyrostat with five degrees of freedom are investigated in detail. The periodic motions of the torque-free symmetrical gyrostat are derived in terms of elliptic functions. The necessary conditions for the occurrence of chaotic oscillations of the disturbed, suspended gyrostat, either dissipative or conservative, are obtained via the Melnikov-Holmes-Marsden integrals. The MHM integrals built on the homoclinic orbits of the torque-free gyrostat and excitation-free spherical pendulum are utilized to establish the transversal homoclinic intersections between the stable and unstable manifolds of the associated Poincare map of the investigated system with perturbations. The results of the theoretical analyses are cross-checked with numerical simulation.