Nonlinear normal modes of a tethered satellite system of two degrees of freedom under internal resonances

The aim of this study was to investigate the nonlinear normal modes (NNMs) of an in-plane tethered satellite system (TSS) during state-keeping phase. The equations of the in-plane motion are derived for the TSS, and the analytic solutions under the three-to-one and one-to-one internal resonances are obtained by applying the method of multiple scales expressed in matrix forms. It is indicated by studying the stability properties of the NNMs that the number of NNMs is more than one over a wide range of the detuning parameter under both internal resonances. Finally, several numerical simulations are made to verify the analytical results.