Nonlinear Dynamics of Two-Body Tethered Satellite Systems: Constant Length Case

The equations governing the three-dimensional motion of a two-body tethered satellite system are highly nonlinear, and their solutions are likely to exhibit interesting behavior typical to nonlinear systems. In this paper, these equations are analyzed using numerical tools such as phase portraits, spectral analysis, Poincare sections and Lyapunov exponents. Motion in the stationkeeping phase (when the tether length is constant) is studied, first considering the in-plane pitch motion only, and then considering the three-dimensional coupled pitch and roll motions. Regions of both regular (periodic or quasi-periodic) and chaotic motion are observed to exist in the planar system for only elliptic orbits, but in the case of coupled motion for both circular and elliptic orbits. The size of the chaotic region grows with eccentricity, and in the coupled motion circular orbit case with increasing values of the Hamiltonian.