Motion of a rigid body with an attached spring-mass damper

Abstract

The stability of motion of a torque-free rigid body with a precession damper is investigated. The equations of mo-tion are presented and nondimensionalized, and the well-known conditions for asymptotic stability of the major axis spin are stated. Attention is given to the cases where these conditions are not met. Results of numerical integration are used to identify three distinct types of motion, including solutions that are apparently limit cycles. Bifurcation diagrams are used to argue that the apparent limit cycles are actually slowly approaching an equilibrium. The bifurcation diagrams also identify regions where the jump phenomenon may occur. The Lyapunov-Schmidt re-duction technique is used to obtain a simple analytical relationship between the system parameters that determines whether the jump phenomenon is possible.