Attitude Dynamics of Satellites with Flexible Appendages- A Brief Review

E demand on precise orientation of a satellite, relative to an inertial or an orbiting frame of reference, has resulted in a whole new area of scientific endeavor referred to as attitude dynamics. In the early stages of space exploration when spacecraft tended to be small, mechanically simple, and essentially inflexible, the elastic deformations were relatively insignificant. Numerous investigations involving active and passive stabilization procedures and accounting for internal as well as external forces have been carried out assuming satellites to be rigid.* However, in a modern space vehicle carrying lightweight deployable members, which are inherently flexible, this is no longer true. Motivations for this trend are many. 1) Every satellite goes through "a brief interval of vigorous acceleration and vibration during boost, followed by a prolonged functioning in a quiescent mode of operation characterized by extremely small loads and acceleration." The universal solution to this dilemma has been to design large members (solar panels, booms, antennas, etc.) as flexible bodies that can be stored in a compact fashion (and hence behave like rigid bodies) during the launch but emerge like a butterfly from its cocoon after the boost terminates. 2) In response to demanding mission requirements, satellite configurations have become increasingly complex to maintain a delicate balance between diverse constraints of space, weight, performance, control, and their optimum realization. For example, ever-increasing demand on power for operation of the on board instrumentation, scientific experiments, communications systems, etc., has been reflected in the size of the solar panels. It has increased to a point where their flexibility can no longer be neglected. For example, the proposed Canadian Communications Technology Satellite (CTS), to be launched in 1975, is designed to carry two solar panels, 3.75 ft x 24 ft each, to generate 1.2 kw. ~ 8 3) Use of larger members may be essential in some missions. For example, Radio Astronomy Explorer (RAE) Satellite' used four 750 ft antennas for detecting low-frequency signals. 4) Certain multipurpose missions, particularly those requiring simultaneous relative measurements from points appreciably apart, may find elastically supported or the recently proposed cable connected multibody systems attractive." 5) Modular construction leading to a gigantic space station through elastic linkages can no longer be considered a fantasy. In this connection, studies of far-reaching significance by Roberson, Wittenburg, and others are of particular relevance."" 6) For longer life span, passive or at least semi-passive attitude control procedures are ideal. They normally involve use of long booms, large radiation reflectors, or aerodynamic flaps." The structural flexibility may interact with attitude control systems of spacecraft in a variety of ways. A NASA special report focuses attention on the significance of this problem through a discussion of the anomalous behavior of several spacecraft. Besides citing useful references, it represents, with several others,' excellent review of the work in this area and puts current and anticipated problems in proper perspective. Furthermore, there are a few recommended procedures for analysis, simulation, and design. A paper by Noll et al. effectively summarizes the NASA document. Experience to date suggests that in most cases problems arise not because of a lack of available analytical/numerical design procedures but because of failure on our part to recognize and appreciate the mechanism of the attitude control/structural flexibility interactions. The review papers just mentioned serve as an ideal introduction to the subject. They effectively summarize dynamical problems through illustration of several past and projected configurations where flexibility played or is likely to play an important role. The problem of flexibility is neither of a recent origin nor is it restricted to spacecraft. Missile, aircraft, and surface vehicle designers have long been dealing with it. As pointed out by Ashley, several of the techniques are directly applicable here. In many ways, however, spacecraft differ from other dynamical systems and require development of modified approaches specifically suited to the emerging field of astroelasticity. However,