Tethered satellite systems: A challenge for mechanics and applied mathematics

Abstract

Tethered satellite systems that is two or more satellites in orbit connected by thin long cables, pose a number of challenging problems in mechanics concerning modeling and derivation of the equations of motion and in applied mathematics, concerning the numerical simulation of their dynamics, deciding on stability of relative equilibria and the proof of chaotic dynamics. We also compare for the practically important process of deployment of one satellite from another satellite uncontrolled deployment with steered deployment, according to Pontrijagin's Maximum Principle. Related to the stability of relative equilibria, as example the Space elevator, which is a tethered system extending from the surface of the Earth beyond geostationary height, is considered.