On the Stability of Spinning Flexible Satellites

Abstract

The attitude stability of spinning flexible satellites in a force-free environment is analyzed. The satellite is modeled by a rigid core body and two symmetric flexible radial beams with rigid tip bodies. Liapunov and Krasovskii stability theorems are employed using the Hamiltonian of the systems as a Liapunov functional. The definiteness checking of the Hamiltonian is complicated due to the fact that it contains the elastic deformations. This problem is solved by applying the modal analysis. Both, symmetric and asymmetric modes are taken into consideration. To determine the eigen-functions of the rotating beam particular attention has to be paid to the dynamic boundary condition which depends on natural frequencies due to the tip body. The sufficient conditions for asymptotic stability obtained include the well known rigid body stability criteria, the well known “energy-sink” criteria, and in addition, new criteria depending essentially on the flexible properties of the system. Moreover, the influence of the number of the considered eigenfunctions is investigated with respect to the stability boundary.