Partial stabilization of an orbiting satellite model with a flexible attachment

We consider a mathematical model of an orbiting satellite comprising a perfectly rigid carrier body and a flexible boom operating under the influence of the orbital moment of the gravity gradient. This model is represented by a nonlinear control system which includes ordinary differential equations governing the carrier body’s angular velocity and attitude quaternion coupled with the Euler – Bernoulli equations that describe the vibration of the flexible component. We propose an explicit feedback design aimed at guaranteeing the partial stability of the closed-loop system in an appropriate Hilbert space.