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A Stability study of gravity oriented satellites Brereton, Robert Cloudesley

Abstract

The stability of gravitational gradient oriented satellites is examined by considering four simplified models. The investigation is carried out numberically and analytically. The techniques employed involve considerable computation and hence are particularly suited to solution by a digital computer. The analysis of the planar motion of a rigid satellite leads to the concept of an invariant surface or integral manifold. Numerical integration of the equation of motion is employed to determine the manifolds. It is shown that for specified values of the parameters describing the satellite, the region in phase space that is consistent with stable motion corresponds to the largest invariant surface which can be found. It is also demonstrated that the manifolds are intimately connected with periodic solutions of the equation of motion and this knowledge permits determining limits on the parameters so as to ensure stable motion by a study of the solution of the variational equation. Several charts suitable for design purposes are presented. The planar motion of a satellite containing a damping mechanism is studied using a simplified model. It is shown that for small dampers the motion eventually becomes nearly identical with a periodic solution of the undamped case. The third model represents a flexible satellite free to deform under the influence of solar heating. An analysis of the temperature distribution in the structure permits determination of the shape of the satellite solely in terms of its position. The resulting equation of motion is derived and it is shown that flexibility does not greatly affect the stability pro- vided that the flexible member is not too long. The case of an axi-symmetric satellite in a circular orbit is also considered. It is shown that in this case manifolds also exist although in some cases apparently ergodic motion can occur. Stability can be guaranteed if the Hamiltonian is less than a prescribed value. Values of the Hamiltonian larger than this may also permit stable motion and in this case an invariant surface is always described in phase space. The stability of the general motion is somewhat greater than that for the planar motion. Charts are presented giving the maximum permissible disturbances for stable motion.

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