Abstract
Three special classes of equilibrium orientations of gyrostat satellites subject to gravitational torques have been treated in the literature. Here we find the set of all equilibria for a restricted class of gyrostat configurations. Those configurations for which the internal angular momentum vector (or the rotor axis) is aligned with a principal axis have been treated in a separate work, where it is shown that at one, and only one, rotor speed there exists a continuum of equilibrium orientations. When the rotor axis is moved away from a principal axis in such a way that it is contained in a plane formed by two principal axes, it is shown that the continuum disappears, and we have a new set of eight equilibrium orientations which have not previously been described. The stability of these orientations is then investigated using the Hamiltonian as a Liapunov testing function. For properly chosen satellite inertia ratios some of these orientations are stable, and might be used in future gravitygradient stabilized satellites.
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References
Anchev, A. A.: 1966, ‘Flywheel Stabilization of Relative Equilibrium of a Satellite’,Kosm. Issl. 4, 192–202.
Likins, P. W. and Roberson, R. E.: 1966, ‘Uniqueness of Equilibrium Attitudes for Earth-Pointing Satellites’,J. Astronaut. Sci. 13, 87–88.
Longman, R. W.: 1969a, ‘A Generalized Approach to Gravity-Gradient Stabilization of Gyrostat Satellites’, The RAND Corporation, RM-5921-PR.
Longman, R. W.: 1969b, ‘The Equilibria of Orbiting Gyrostats with Internal Angular Momenta Along Principal Axes’, Proceedings of the Symposium on Gravity Gradient Attitude Stabilization, Aerospace Corporation Report No. TR-0066(5143)-1 (Air Force Report No. SAMSO-TR-69-307). Also available as RAND Corporation P-3916, Aug. 1968.
Longman, R. W. and Roberson, R. E.: 1969, General Solution for the Equilibria of Orbiting Gyrostats Subject to Gravitational Torques’,J. Astronaut. Sci. 16, 49–58.
Pringle, R., Jr.: 1966, ‘On the Stability of a Body with Connected Moving Parts’,AIAA J. 4, 1395–1404.
Roberson, R. E.: 1968, ‘Equilibria of Orbiting Gyrostats’,J. Astronaut. Sci. 15, 242–248.
Roberson, R. E., and Hooker, W. W.: 1967, ‘Gravitational Equilibria of a Rigid Body Containing Symmetric Rotors’, inProc. 17th Congr. Int. Astronaut. Fed. (Madrid, 1966), Dunod, Paris.
Rumiansev, V. V.: 1967a, ‘On the Stability of Stationary Motions of a Satellite with a Rotor and Cavity Containing Fluid’,Kosm. Issl. 5, 163–169.
Rumiansev, V. V.: 1967b, ‘On Stability of Stationary Motions of the Gyrostat-Satellite’,Proc. 18th Congr. Int. Astronaut. Fed. (Beograd, 1967), to appear.
Zajac, E. E.: 1964, ‘The Kelvin-Tait-Chetayev Theorem and Extensions’,J. Astronaut. Sci. 11, 46–49.
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This research is sponsored by the United States Air Force under Project RAND-Contract No. F44620-67-C-0045-monitored by the Directorate of Operational Requirements and Development Plans, Deputy Chief of Staff, Research and Development, Hq. USAF. Views or conclusions contained in this study should not be interpreted as representing the official opinion or policy of the United States Air Force. The material presented here was originally published in RAND Corporation Memorandum RM-5921-PR. The author wishes to acknowledge his indebtedness to Dr. R. E. Roberson for helpful discussions, and for suggesting a research area, part of which is treated here.
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Longman, R.W. Gravity-gradient stabilization of gyrostat satellites with rotor axes in principal planes. Celestial Mechanics 3, 169–188 (1971). https://doi.org/10.1007/BF01228031
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DOI: https://doi.org/10.1007/BF01228031