Elastic oscillations of the space elevator ribbon

The space elevator is likely to offer an alternate and efficient method for space travel. The main component of the space elevator is the tether (or the ribbon), which extends from the Earth to an equatorial satellite beyond the geosynchronous altitude and is fixed to a base on the surface of the Earth at its lower end. This paper studies the elastic oscillations of this ribbon. The elastic deformations are discretized using a set of admissible basis functions, and the Lagrangian approach is used to derive the equations of motion ofthis discrete system. For small motions, the longitudinal extension and transverse displacement of the ribbon can be analyzed separately. Longitudinal and transverse modal frequencies and corresponding modes are calculated numerically, assuming typical values for the properties of the ribbon.