Application of Computer Algebra to Investigation of Equilibrium Orientations of Satellite Subject to Gravitational and Constant Torques
The equilibrium orientations of a satellite in a circular orbit under the influence of gravitational and constant torques are investigated. The stationary motions of a satellite are governed by a set of nonlinear algebraic equations. A computer algebra method based on algorithm for the construction Groebner basis is proposed for determining the equilibrium orientations of a satellite with a given constant torque vector and given principal central moments of inertia. It is shown that 24 isolated equilibrium orientations exist when the module of constant vector is sufficiently small. The equilibrium orientations are determined by algebraic equation of the sixth degree and are analyzed numerically.
INFLUENCE OF CONSTANT DISTURBING TORQUES ON THE MOTION OF GRAVITY-GRADIENT STABILIZED SATELLITES
Abstract : The effect of a constant disturbing torque upon the transient response of a gravity-gradient stabilized body is demonstrated. It is assumed that the satellite is on a circular orbit. Thus the oblateness and other asymmetries of the earth are neglected. The only torques which act on the body are those due to the gravity gradient, and the contant disturbance. (Author)
Canonical representatives for residue classes of a polynomial ideal
At the EUROSAM Conference 1974 it was conjectured that there exist probably no canonical forms for polynomial expressions under polynomial side relations. In 1965, however, Buchberger had already implemented a reduction algorithm solving the problem over fields. Positive results were also attained independently since 1974 by R. Shtokhamer and the author. In this note a general theorem on canonical representatives is obtained and by application to Buchberger's and Shtokhamer's algorithms it is proven that the stated problem is solved.