Dynamics of a partial space elevator with multiple climbers

A space elevator has been proposed as an alternate method for space transportation. The materials currently in existence are not strong enough to support the stresses generated in a full structure; the use of a partial elevator may be considered instead, at least for the near term. For a sufficiently long ribbon/tether floating in space, a payload can dock at its lower end, use a climber to ascend to higher altitudes and then be launched, thereby saving in fuel consumption. Since this structure can be modelled as a multiple-body system with a very long tether, the dynamics of such a system is studied in this paper. In the first part, the equations of motion are derived using the Lagrangian approach, and then linearized in order to determine the libration frequencies. In the case where a single climber is in use, the governing equations are solved numerically; it is noted that the motion of the climber introduces oscillations in the tether, thus introducing errors into the desired orbit of the payload. In the second part, the use of multiple climbers is investigated in an attempt to minimize these errors.