Control of Beams and Chains Through Distributed Gyroscopes

The control of deformable bodies through a large number of small gyroscopes has received attention in the past 20 years. Promising in principle for the control of spacecraft structures, the idea needs the design of fit control algorithms to be developed in practice. Aiming at this design, here we develop two special but technically important cases, which can be easily implemented and of possible use in spacecraft appendages: an elastic beam with an embedded array of coaxial rotors distributed along the beam's axis and spinning about it, and a chain, each rigid link of which contains a rotor whose axis is pinned along the link-to-link direction. We show some results for the dynamics or such structures that are made possible by the control of the rotors and can be implemented to deal with and eventually damp small disturbances: the propagation of screw waves of small amplitude through chains or beams, and the diversion of energy from one mode to another in the linear transversal vibrations or beams.