Nonlinear Dynamics of a Space Vehicle with an Attached Elastic Rod System

The nonlinear dynamics of a flat rod system is considered. The system consists of elastic inextensible rods, the ends of which are connected by elastic-viscous nodal hinges allowing large rotation angles. The rod system is attached to a non-deformable space vehicle rotating relative to its centre of gravity and moving along the horizontal and vertical axis as a free rigid body. The motion of such a system is described in the moving coordinates system. The displacements of each rod are characterized by the rod’s finite rotation as a rigid body relative to a straight line passing through two neighboring hinge nodes, and by the bend with a small lateral displacement. The motion equations are obtained in velocities for the space vehicle, and in the selected generalized coordinates for the rod system based on the principle of possible displacements. The calculation examples with the analysis of convergence when integrating nonlinear systems of differential equations are presented. The method of simplifying the calculations by reducing the rod masses to nodal masses in hinges is described, with necessary explanations and justifications.

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