Bifurcations and stability of amplitude modulated planar oscillations of an orbiting string with internal resonances

Nonlinear free transversal oscillations of an orbiting string satellite system are analyzed. They are governed by two partial integro-differential equations with quadratic nonlinearities. The system is weakly nonlinear but in practice works in conditions of nearly simultaneous internal resonance. The ability of truncated models to capture specific phenomena is discussed. By limiting the investigation to the planar motion with a one prevailing component perturbed out-of-plane, two different models with three modes in primary and secondary resonance are adopted. For increasing levels of the system energy, fundamental and bifurcated paths of fixed points are obtained and their stability is investigated. Moreover, periodically amplitude modulated planar motions and their stability for out-of-plane disturbances are studied.