General Solution for the Equilibria of Orbiting Gyrostats Subject to Gravitational Torques.

Richard W. Longman, R. E. Roberson

Expert InsightsPublished 1968

Theoretical design principles for maintaining orbital stability of rigid satellites having one or more symmetric rotors. Considering the internal angular momentum to be variable in direction and magnitude, and considering circular orbits only, all possible orientations within the orbiting reference frame are found that remain unaltered by inverse-square gravitational torque over time. These are functions of the moments of inertia of the gyrostat and the relative angular momentum of the rotor(s) with respect to the satellite. The matrix equation is put into a form from which it is found that orbital stability can be achieved by proper choice of the internal angular momentum vector. There is a two-parameter family of such orientations. If the direction of the geocentric is vertical with respect to principal axes of the body, a unique equilibrium orientation for each direction is obtained. When spacecraft attitude is taken into account, results are the same except for a slight change in the relative angular momentum. 34 pp. Refs. (See also P-3916.) (MW)

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  • Copyright: RAND Corporation
  • Availability: Web Only
  • Year: 1968
  • Document Number: P-3915

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Longman, Richard W. and R. E. Roberson, General Solution for the Equilibria of Orbiting Gyrostats Subject to Gravitational Torques. Santa Monica, CA: RAND Corporation, 1968. https://www.rand.org/pubs/papers/P3915.html.
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