Comments on "Energy Considerations for Attitude Stability of Dual-Spin Spacecraft"

Abstract

N a recent Note,1 Prof. Fang obtains criteria for stability of an equilibrium motion of a dual-spin spacecraft by determining whether equilibrium motion corresponds to minimum energy state of permissible motions. The equations he employs to determine minimum energy state treat dual-spin spacecraft as consisting of a rigid symmetric rotor, body S, which rotates relative to a rigid asymmetric body, body A, in a force-free field. The axis of relative rotation between two bodies corresponds to axis of symmetry of rotor and to a principal axis of body A. It is assumed that no net torque is exerted about this axis between two bodies. Although admittedly not modeled in his equations, he states that analysis is made with assumption that the bodies A and S possess some degree of flexibility and some internal dissipative mechanism, and leaves reader with incorrect impression that his results are generally valid for this case (possibly excepting highly flexible spacecraft). In fact, it is possible to make conclusive statements about stability of equilibrium solution only for particular equations being examined regardless of method of analysis. Extending results for this case to same equilibrium solution for other, more complex, equations (multibody or flexible body equations) is at best an intuitive and heuristic procedure and can be only approximate. Even though this type of analysis is not rigorous, stability criteria gained thereby are still useful as a rule of thumb to guide more exact analyses or spacecraft design choices. Similar forms of this type of analysis have been performed by lorillo 2 and Likins3 for dual-spin spacecraft. Fang references Likins' paper and employs his spacecraft model and, to a large extent, notation. His results, however, differ from those of Likins (and lorillo, whom Likins has followed). Fang's results are those that would be obtained for energy dissipation on body A only, and agree with those of Likins for this special case only. The stability of equilibrium solution coi = 0, co2 = 0, cos5 = const, co3A = const (1) is examined. The stability criterion is given by Likins as (PA/XA) + (Pa/X fl) < 0