Lyapunov stabilization of spinning multibody systems driven by an active/passive PD-feedback control law

For a class of spinning mechanical systems, this article investigates the stability domain of the spun-pose equilibrium state as a function of the commanded spin-rate, which is assumed constant. In order to unify the modelling paradigm with the closed-loop stability analysis, a generalized time-varying Lagrangian function is introduced that simultaneously accounts for both passive PD-feedback (e.g. springs/dashpots) and active PD-feedback (e.g. spin-angle tracking control).