Orbiting chains and rings

Two very different, highly flexible, space structures proposed during the last decade which involve analytical solution of certain partial differential equations are discussed. The first structure is an array, or hanging chain of aluminum beads which would serve as a convenient communicator if, under the influence of the Earth's gravity gradient, it assumes a local vertical orientation as it circles the Earth. Two passive schemes have been proposed for damping the rigid modes: twist the wire at the ends to provide non-zero moment of inertia about the vertical, thereby inducing relative motion of the two tips during rigid pitch or roll, and thus exercising a damper; and introduce weak lossy springs between the end sections and the main section; thereby providing linear coupling between the springs and all the in-plane (pitch) modes. The second structure is a complete ring of satellites cabled together at synchronous altitude. By a slight increase in altitude, the cable is in tension. This configuration is, however, unstable, and an active feedback control scheme is required to stabilize it. A possible scheme involves local cable length adjustment based on measurement of local altitude and shape variations and their rates.