THE EQUILIBRIA OF ORBITING GYROSTATS WITH INTERNAL ANGULAR MOMENTA ALONG PRINCIPAL AXES,
Abstract
This paper finds all orientations, that are in equilibrium relative to gravitational torques, for a gyrostat satellite whose internal angular momentum (or whose rotor axis) is along a principal axis of the body. It is found that for sufficiently small rotor speeds there are twenty-four discrete equilibrium orientations which coincide with the equilibria of a rigid body when the rotor speed goes to zero. These are the case 1, 2, and 3 solutions described in the literature. As the rotor speed is increased these discrete solutions disappear, four at a time, until one is left with only those equilibria which have the rotor axis aligned with the perpendicular to the orbital plane. However, it is discovered, for unsymmetric satellites with the rotor axis along the axis of greatest or least moment of inertia, that there is a critical rotor speed at which there exist two continua of equilibrium orientations (which contain the case 2 and 3 solutions for this rotor speed). If these are stable and if there are perturbing torques present, a gyrostat that is initially in one of the equilibrium orientations of a continuum will immediately begin rotating along the continuum. This means that the satellite will tumble. Such behavior resembles the observed anomalous behavior of some gravity gradient stabilized satellites that use long, flexible booms. Thus, the continua offer a possible explanation of the observed instabilities for these satellites. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1968
- Accession Number
- AD0675980
Entities
People
- Richard W. Longman
Organizations
- RAND Corporation