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Dynamics of a large class of satellites with deploying flexible appendages Lips, Kenneth Wayne


A general formulation is presented for the librational dynamics of satellites having an arbitrary number, type, and orientation of flexible appendages, each capable of deploying independently. In particular, the case of beam-type appendages deploying from a satellite in an arbitrary orbit is considered. The governing nonlinear, nonautonomous, coupled system equations are not amenable to any closed form solution, hence are integrated numerically using a digital computer. Effect of important system parameters is assessed through illustrative configurations representing a large class of gravity gradient and spinning spacecraft. Rather than accumulation of a large amount of data, the emphasis is on evolution of a generalized and organized methodology for coping with such complex dynamical systems. The analysis examines the degree of interaction between flexibility, deployment, and attitude motion through systematic variation of system parameters. A study of appendage vibration characteristics suggest that an orbiting beam cannot be treated simply as a rotating beam because of the presence of the gravitational field. Rate of rotation plays a dominant role in stiffening the beam as evidenced by the noticeable straightening of the eigen-functions for even relatively low spin rates (2 rpm). Results also show that the deployment-related Coriolis force can play a major role in causing large in-plane deformations. This implies that, in some cases, deployment should be carried out in stages so as to limitthe time available to build up large amplitude oscillations. Investigation of librational response shows that the coupled character of the motion can significantly affect system dynamics, hence caution should be exercised in utilizing results based on simplified planar analyses. Depending on orbital parameters and physical properties of booms, there are critical values of appendage length and deployment rate for which the satellite can tumble over. On the other hand, in general, appendage offset and shifting center of mass were found to have insignificant effect on response for the cases considered. This may permit considerable simplification of the complex hybrid equations with associated saving in computational time and effort. Also, the small amplitude oscillations evident both with the gravity gradient and spin-stabilized configurations tends to substantiate the adoption of a linear vibration analysis. The simulation of such diverse classes of satellites with relative ease demonstrates the versatility of the formulation.

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