GENERAL SOLUTION FOR THE EQUILIBRIA OF ORBITING GYROSTATS SUBJECT TO GRAVITATIONAL TORQUES,
Abstract
Three special classes of equilibrium orientations of orbiting gyrostats subject to gravitational torques have been treated in the literature. Considering the internal angular momentum of the gyrostat to be variable in direction and magnitude, we find here all possible equilibria both for the restricted problem (where the effect of spacecraft attitude on the translational equations is ignored) and for the unrestricted problem. The matrix equation which must be satisfied for an equilibrium is put in a particularly illuminating form, from which is found a simple necessary and sufficient condition that an orientation can be made an equilibrium orientation by proper choice of the internal angular momentum vector. It is found that there is a two-parameter family of such orientations. In particular, if the parameters are chosen to describe the direction of the geocentric vertical with respect to principal axes in the body, then one obtains a unique equilibrium orientation for each direction so chosen. A simple geometric visualization of all solutions is presented in these terms. Also, a fourth special class of equilibria is discussed in which the body axis of intermediate moment of inertia lies in the orbital plane. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1968
- Accession Number
- AD0675979
Entities
People
- Richard W. Longman
- Robert E. Roberson
Organizations
- RAND Corporation