Nutational stability of an axisymmetric body containing a rotor

Abstract

T7K)R many satellite and space-probe missions, full three--F axis attitude control is not required, and simple (passive) spin stabilization is sufficient to insure satisfactory system performance. In many applications, in fact, the need for stabilization is not dictated by primary mission requirements at all but arises indirectly, perhaps as a means of minimizing or removing thermal and antenna design problems. Spin control is ideal for this type of mission. In other caess, considerable improvement in system performance is afforded, e.g., in a high-altitude communication satellite, increased antenna gain can be obtained using an antenna with a toroidal radiation pattern.Fully passive techniques for three-axis attitude control have only limited application, and it is generally necessary to employ far more sophisticated, active stabilization methods such as mass expulsion or flywheel control systems. However, there is one active, but fairly simple, three-axis control technique that is a natural extension of spin stabilization. In this technique, control of the third axis (control about the spin axis) is achieved by "despinning" a portion of the spinning spacecraft. That is, instead of the vehicle being a single body, it is constructed of two bodies (I and II in Fig. 1) constrained to rotate about a common axis. Suppose that II is the despun portion. A motor (not shown) is included which can change the relative rate about OZ. If the motor is servo-controlled, say by a sensor mounted on one of the bodies, the rate of body II can be maintained at zero or can be varied to permit a given axis in II, normal to OZ, to track an external reference. Thus, in effect, the despun component is three-axis stabilized by means of a single-axis active controller. Control of spin-axis attitude, if required at all, would normally be by ground command to activate, for example, pulse jets, or, in the case of earth orbiters, a magnetic coil mounted on the spinning component.A wide range of configurations can be devised which use this basic two-body construction. One application is id the use of a small directional antenna as the despun portion of a spin-stabilized communications satellite. In this application, the spin axis would be maintained normal to the orbit plane, and the antenna controlled to point along local vertical, allowing maximum gain to be obtained.Another type of single-axis control can be provided if the major part of a spacecraft is despun, and a high-speed internal rotor is employed to provide the gyroscopic stiffness. In fact, this case can be considered a derivative of a three-flywheel system from which two wheels are removed and the third operated about a high bias rate instead of null. Because of the high speed of the internal rotor, spin-axis pointing can again be controlled by ground command.The two-body configuration does appear to offer definite advantages as a means of achieving simplified three-axis attitude control of spacecraft; for this reason, it has received, and is receiving, serious attention in the in...

Nutational stability and core energy of a quasirigid gyrostat

“…As was first pointed out in Ref. 5, if the energy-sink analysis is to be applied correctly, we must take into account the power expended or absorbed by the motor; otherwise, one arrives at an erroneous conclusion. The preceding section best illustrates this for the case when the rotor is maintained at a constant relative speed.…”

“…As first noted in Ref. 5, the essence of the energy-sink idea is still valid even in the presence of possible energy sources, as long as the energy source (motor) is properly taken into account. This is an easy task when one part of the two-body system is rigid and axisymmetric; Euler's dynamical equations may be used for the rigid part of the system and axisymmetry eliminates the gyroscopic term.…”

“…A primary source of debate has been the argument that the energy-sink approach is invalid for systems containing driven rotors since the motors could act as energy sources. 6 ' 7 As early as 1964, Landon and Stewart 5 had addressed this problem, and by subtracting the work done by the motor torque from the kinetic energy, they effectively showed that the results continue to hold; however, this concept appears to have been overlooked because of their "restrictive analysis" and the debate continued.…”

“…5 in showing the validity of the method in the presence of a motor torque. This analysis begins by showing exactly why the conclusions of Ref.…”

“…INCE the pioneering work of Vernon D. Landon, establishing stability criteria for the class of "slightly nonrigid" or quasirigid spacecraft has received widespread attention, 1 ' 5 particularly the heuristic "energy-sink" analysis. However, over the years, fueled by a "lack of rigor" in the analysis, the approach has incited considerable debate, 6 ' 10 sometimes because of the interpretation of the method.…”