Bifurcations of relative equilibria of an oblate gyrostat with a discrete damper

We investigate relative equilibria of an oblate gyrostat with a discrete damper. Linear and nonlinear methods yield stability conditions for simple spins about the nominal principal axes. We use analytical and numerical methods to explore other equilibria, including bifurcations that occur for varying rotor momentum and damper parameters. These bifurcations are complex structures that are perturbations of the zero rotor momentum case. We use Lyapunov–Schmidt reduction to determine an analytic relationship between parameters to determine conditions for which a jump phenomenon occurs. This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States