Certain space missions (e.g., GEOS-3, GALILEO) require the deployment of a flexible linkage from a relatively rigid spacecraft. Questions such as the following arise regarding the behavior of the spacecraft during the subsequent to deployment: How does the deployment process affect pointing accuracy? What is the maximum deployment rate that does not give rise to interferences resulting from structural deformations? What control laws should be used for the deployment process?; To answer such questions, one may employ numerical simulations based upon equations governing the motion of a rigid body supporting a deployable flexible linkage that carries a rigid load. However, since existing methods for the formulation of equations of motion do not lend themselves well for this purpose, one must extend these methods in order to come into position to undertake numerical simulations. Such an extension is carried out in the present work. The central idea underlying the extension is that equations of motion of a system of bodies subject to constraints can be obtained by temporarily disregarding the constraints, writing expressions for generalized inertia forces and for generalized active forces associated with the unconstrained system, and then using these together with coefficients appearing in the constraint equations to generate a set of equations of motion of the original system.; Certain arrays, called "Z arrays", are introduced in connection with the derivation of constraint equations associated with elastic bodies arranged in closed kinematical loops. Use of these arrays makes it possible to let the linkage have any number of links.; The legitimacy of modal representation of the elastic deformation of a typical link is discussed in view of the fact that the link is subjected to an unknown time-varying shear load.; Several studies are performed to illustrate the behavior of the system with a variety of initial conditions, parameters, and number of modes used to describe elastic deflections. These studies indicate that in-orbit deployment can be obtained passively, and that, in certain applications, weight reduction of the links can be sustained without affecting the dynamic behavior of the system, as far as in-plane motions are concerned.
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