This work presents a  procedure for obtaining systematically the equations of the attitude motion of an important particular class of space crafts: those composed by a central rigid body possessing rigid reaction wheels, and deployable solar arrays, which are considered flexible only after completely opened. The Lagrangian formulation is employed along with the Assumed Modes Method to avoid a hybrid set of equations of motion. A code employing the symbolical software Reduce was developed to obtain, in certain cases, these equations automatically. The set of non-linearized equations of the transient opening phase and the set of equations of the following phase are obtained for a sample satellite applying this Reduce code. For this satellite, the transient phase is studied through the time evolution of its inertia dyadic, and through the attitude motion induced by the deploying arrays. Also, for this example, the impact between the central rigid body and each of the solar arrays is introduced. To the set of linearized equations is coupled a control law accordingly to the Eigenstructure Assignment Technique whose goal is to stabilize the satellite attitude motion and to damp its solar arrays elastic vibrations.
 

Roma, A.M.: Análise dinâmica e controle de um satélite artificial com painéis solares flexíveis, Dissertação de Mestrado em Ciência Espacial, Instituto Nacional de Pesquisas Espaciais, São José dos Campos, 03/1991. Portuguese.