Nonlinear Dynamics and Bifurcations of a Spherical Multi-tethered Lighter-Than-Air System in Uniform and Modulated Flow

Abstract

We investigate the nonlinear dynamics and bifurcations of a spherical multi-tethered lighter-than-air-system (LTAS) in uniform and modulated flow. The dynamical system includes six degrees of freedom for the spherical LTAS which consistently models the coupling between the translational and rotational rigid-body motions. A linear stability analysis reveals the existence of a supercritical Hopf bifurcation with respect to the reduced velocity of the flow, followed by periodic self-excited oscillations. The Hopf threshold is influenced by both the initial tether inclination angle and the rotational damping ratio, offering insights for stability based design. The dynamical system is perturbed by a weakly modulated flow culminating with a nonstationary bifurcation structure that ensures out-of-plane quasiperiodic and chaotic dynamics with respect to the vertical plane exhibiting finite rigid-body rotations.