Nutational stability and passive control of spinning rockets with internal mass motion

Abstract

Necessary and sufficient conditions for asymptotic stability are developed for a symmetric spinning rocket with axial forcing and dissipative internal mass motion. Results show that spin about the axis of least inertia is asymptotically stable provided that three conditions are satisfied: 1) the axial thrust magnitude is sufficiently large, 2) the restoring forces for the internal mass motion are sufficiently large, and 3) the internal mass motion occurs aft of the system mass center. Under these same conditions, spin about the axis of largest inertia may be unstable. Numerical studies show that a passive control device with these characteristics can be used to attenuate the coning of prolate spinners such as those transfer orbit boost vehicles that have been plagued by unexpectedly pronounced coning instabilities. Nomenclature c = damping constant for particle motion F = magnitude of thrust (assumed constant) /i, /i, 73 = moments of inertia of (symmetric) rigid body for axes #1, #2, and 53, respectively k = spring constant for elastic restraint on particle M = mass of rigid body m = mass of particle li = m/(m -f M) Q = nominal spin rate of rigid body about #3 0)1,0)2 = components of rigid-body angular velocity for axes B and B2, respectively