Transient attitude dynamics of satellites with deploying flexible appendages

The paper presents a general formulation for librational dynamics of satellites with an arbitrary number, types, and orientation of deploying flexible appendages. The generalized force term is incorporated making the formulation applicable to a wide variety of situations where aerodynamic forces, solar radiation, earth's magnetic field, etc. become significant. In particular, the case of a beam-type flexible appendage deploying from a satellite in an arbitrary orbit is considered. The corresponding nonlinear, non-autonomous equations for in-plane and out-of-plane vibrations are derived, allowing for the variation of mass density and flexural rigidity along the length with time dependent deployment velocity and spin rate. Next, the attention is focused on the linearized analysis of the in-plane vibrational equation using the assumed-mode method and its substantiation through numerical integration. Finally, the paper presents results for both steady-state and transient attitude behaviour for a representative gravity gradient configuration for a range of initial conditions and system parameters. Results show the combined effect of flexibility and deployment on the dynamics of the system to be substantial. Disturbance of the appendage can excite large amplitude librations. On the other hand, the converse situation is not necessarily true. Furthermore, Coriolis loading, induced by the extending appendages, can become a limiting factor in arriving at a deployment strategy; an effect not pointed out in the literature.