Problem of Unwinding of a Rotating Cluster of Bodies under Zero Gravity

摘要

The problem of unwinding, under zero gravity, of a pair of dynamically identical bodies (dumbbell-shaped spacecraft) connected by an inextensible weightless film wound as a roll around the cylindrical surfaces of the bodies is considered. In the prelaunch position, the axes of these surfaces are parallel to each other and equidistant from the cluster rotation axis. The film winding direction is consistent with the direction of the cluster rotation so that, after the holding locks are opened, the bodies begin to move away from each other under the action of centrifugal forces, thus pulling and unwinding the film. It is assumed that the film median passes through the cluster center of mass. A pair of cords bounding an imaginary film can be used instead of the actual film as well. Some basic relations between the cluster motion parameters in the unwinding process are obtained. A scheme for describing the unwinding of clusters of any number of dynamically identical polygon-shaped bodies is proposed.