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 Torque on Equilibria of Satellite in Circular Orbit
We consider the equilibria of a satellite in a circular orbit under the action of gravitational and constant torques. The number of equilibria depending on the parameters of the problem is found by the analysis of an algebraic equation of order 6. The domains with different numbers of equilibria are specified, and the equations of boundary curves are determined in function of values of the components of constant torque. Classification of different distributions of number of equilibria is made for arbitrary values of the parameters.
Relative Equilibria of a Gyrostat Satellite with Internal Angular Momentum Along a Principal Axis
Abstract A new analytical solution to the problem of determining all equilibria of a gyrostat satellite in a circular orbit is given in the case where internal angular momentum of the gyrostat satellite is collinear to its principal axis of inertia. The number of isolated equilibria is shown to be no less that eight and no more than 24. Sufficient conditions for equilibria stability are obtained.