A THREE-DIMENSIONAL ANALYSIS OF A TANGENTIAL YO-YO DESPIN DEVICE ON A ROTATING BODY

A THREE-DIMENSIONAL ANALYSIS OF A TANGENTIAL YO-YODESPIN DEVICE ON A ROTATING BODYBy Robert L. Collins, Jr.Langley Research CenterSUMMARYThe problem of despinning a rotating rigid body by the release of yo-yo despinweights is considered. Although studies have been made previously for the two-dimensional case of a fixed spin axis, there has been little effort to incorporate an ini-tial coning angle which, in general, leads to a three-dimensional problem. This studyconsiders the effect of an initial coning motion on the parameters which influence thedesign of a yo-yo despin system. The differential equations of motion of the system arederived for a symmetric rigid body and these are integrated numerically to provide solu-tions for several specific cases. The results show that a two-dimensional study is suf-ficient to predict such parameters as cable length, cable tension, and time required todespin, as long as the initial coning angle is less than 10 ° to 30 °, and the masses of thedespin weights are not too small. The parameters plotted in this study give an indicationof the effects of initial coning angle on the design parameters of interest for what iscalled tangential motion.INTRODUCTIONA typical problem area in the design of earth orbiting satellites is the reduction ofthe angular velocity which may occur after injection into orbit. One efficient technique ofdespinning a satellite is by the use of a so-called yo-yo despin device. Basically, thisdevice is a simple arrangement of small masses attached to cables which are wound aboutthe periphery of the spinning body in a plane perpendicular to the spin axis. When it isdesired to reduce the rotational rate of the body, the despin weights are released and theymove away from the body constrained only by the cables which unwrap from the body.The tension produced in the cables causes a moment which reduces the spin rate of thebody. Essentially, the angular rotation of the body is reduced by transferring a desiredquantity of angular momentum from the body to the despin weights. When sufficientangular momentum is transferred to obtain the desired reduced body spin rate, the cablesare released from the body which then rotates in space independent of the yo-yo system.