A three-dimensional dynamic analysis and libration study of a tethered satellites system

By a three-dimensional Lagrangian formulation, an exact set of ten coupled nonlinear second-order differential equations has been derived for a system with an extensible tether connecting two end satellites of distributed mass. The effects of tether mass, small orbital eccentricity, central body oblateness, aerodynamic drag force, and solar radiation pressure are also included in the formulation. By linearizing the exact differential equations, the in-plane (orbital plane) differential equations are found to be decoupled from the out-of-plane ones. The characteristic equation of the in-plane differential equations is derived and some associated stability constraints are shown.