The tethered satellite system is characterized by weak nonlinearities but it practically works in conditions of internal resonance which produces unstable oscillations. The effect of a longitudinal control force is investigated. Since the displacement component in the orbit plane is always present in the motion due to the nonlinear coupling, the control force is assumed depending only on this component and also when a prevailing out-of-plane oscillation is considered. The harmonic balance method and numerical solutions of amplitude modulated equations are used to obtain stationary and nonstationary oscillations, respectively; the Floquet theory is followed in the stability analysis. The assumed control force is shown to be effective in reducing the primary and secondary instability regions of oscillations perturbed by internally resonant disturbance components. © 1995.
Vestroni, F., Luongo, A., & Pasca, M. (1995). Stability and control of transversal oscillations of a tethered satellite system. Applied Mathematics and Computation, 70(2–3), 343–360. https://doi.org/10.1016/0096-3003(94)00114-J