Momentum Transfer Dynamics of a Gyrostat With a Discrete Damper1

The stability of motion of attitude maneuvers of a torque-free rigid gyrostat with a discrete damper is investigated. The equations of motion are presented and non-dimensionalized, then rewritten as a singularly perturbed, noncanonical, Hamiltonian system. Conditions for equilibrium motions and for their stability are developed. Bifurcation diagrams are used to illustrate the stable and unstable branches of steady spins, and these bifurcation diagrams are interpreted in the slow state space of the rotor momenta and the unperturbed system Hamiltonian. Numerical integration is used to compute representative momentum transfer trajectories, which are also interpreted as projections onto the slow state space. We are especially interested in identifying regions of phase space through which momentum transfer maneuvers might reasonably be expected to succeed, but which are destabilized by the presence of the damping mechanism.