Longitudinal vibration of gravity-stabilized, large, damped spacecraft modeled as elastic continua

Abstract

Longitudinal vibration of gravity-stabi lized, structurally damped, large flexible satellites undergoing pitching librations in circular and elliptic orbits is studied. Stability analysis of the linearized system indicates 1) that vibrational stability is ensured if p>V3, and 2) that structural damping plays a role in exciting the pitch motion in eccentric orbits. Analytical expressions are derived for stability boundary and response of vibration in evennumbered modes in circular orbits using perturbation methods. They indicate that parametric resonance can occur at two additional frequencies, and the minimum (critical) damping necessary to avoid vibrational instability is sensitive to the satellite inertia ratio. An attempt is made to establish stability of the nonlinear system using the Hamiltonian of the corresponding conservative system. The stability criterion thus obtained gives a conservative estimate of the stability boundary. Numerical simulation verifies the results of the stability analysis and indicates that parametric resonance occurs only in the even-numbered modes. It is also found that the nonlinear effects arising out of vehicle flexibility do not seem to produce significant deviation either in rigid-body motion or stable vibrations.