ON THE DYNAMICS OF THE DEPLOYMENT OF A TETHER FROM AN ORBITER .2. EXPONENTIAL DEPLOYMENT

In this paper an analysis of the exponential deployment of a tether ha s been carried out taking into account the following assumptions: the orbiter is in a circular orbit; the Earth has a spherical gravitationa l potential; the tether is flexible, non-extensible, and the deployed mass is negligible compared with the mass of the orbiter. A phase-plan e (theta, theta) has been considered and four steady solutions have be en found, in which the tether forms a constant angle with the vertical . They appear as critical points of the phase-plane: two unstable (sad dle) and two stable (foci or nodes). It is shown that it is possible t o leave out the tether aligned with the vertical, at rest, that is, wi thout later libration, by means of a two-stage deployment process: a f irst stage in which the tension is controlled-indirectly-to get a cons tant radial velocity of the end mass (l = 1); a second stage in which the tension is controlled-indirectly as well-to get a constant ratio ( l/l) (exponential deployment). In both phases the tether unwinds from a reel whose angular velocity must be controlled. The essentially stab le character of deployment gives robustness to this open loop strategy , because the effects not considered produce small departures from the nominal law, resulting in a residual, negligible libration. Moreover, the proposed deployment scheme can be taken as a starting point for m ore elaborate strategies (in a closed loop for example).