The Equilibria of Orbiting Gyrostats with Internal Angular Momenta Along Principal Axes.

by Richard W. Longman

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A companion paper to P-3915, offering a possible explanation for the tumbling of some gravity-gradient-stabilized satellites that use long flexible booms. At small rotor speeds, an orbiting gyrostat with rotor axis along a principal body axis has 24 discrete orientations that are in equilibrium relative to gravitational torques. With increasing rotor speed, these disappear four at a time, leaving only those equilibria that have the rotor axis aligned with the perpendicular to the orbital plane. For unsymmetric satellites with the rotor along the axis of greatest or least moment of inertia, there is a critical rotor speed, at which there are two continua of equilibrium orientations. If these are stable, and if perturbing torques are present, the gyrostat will immediately start rotating along the continuum. The sudden appearance of a continuum at one rotor speed is surprising; however, it can be explained by viewing the introduction of angular momentum as changing the inertia matrix to one corresponding to a symmetric body. (Prepared for the SAMSO-Aerospace Gravity Gradient Attitude Control Symposium, Los Angeles, December 3-5, 1968.) 40 pp. Refs. (MW)

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