The stability of a gravity gradient satellite with a rigid main body and elastic antennas is studied using Liapunov's Direct method. The complete conditions for equilibrium and stability for a particular class of two dimensional models are determined. Previous work restrained the analysis to elastic stability, in the small, and only for equilibrium positions corresponding to zero initial elastic deformation. Although the work presented here is for two dimensional motion, the intent is to bring forth an approach to the determination of the complete equilibrium and stability criteria in the large as well as the small. The effect of different parameters on the equilibrium and stability is also determined. It is shown that: (1) a satellite will always be in equilibrium at 0 and 90 attitude angle positions, (2) a satellite if stable at 0, will always be unstable at 90 orientation and vice versa, and (3) there can exist only one more equilibrium position between 0 and 90, and if so, 0 and 90 will be unstable equilibrium positions and the stability of the third position must be ascertained. A truncated power series is used to approximate the shape of the elastic antennas. The results are compared to those obtained by a more conventional method using the eigenfunctions of the freely vibrating antennas as comparison function. It is found that using the power series 'yields a more conservative stability criteria.

Library of Congress Subject Headings

Equilibrium of flexible surfaces

Publication Date


Document Type


Department, Program, or Center

Mechanical Engineering (KGCOE)


Budynas, Richard


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