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)
An analytical approach to the design of electrodes in high-power, fast-transverse-flow CO2 lasers
Abstract Usually, the design of the electrodes of fast-transverse-flow CO 2 lasers relies more on experimental data than on theoretical analysis. Traditional systems sustain a stable, high-power discharge but the current distribution generates a peaked, non-uniform small-signal-gain pattern. We present a theoretical model suitable for the design of electrodes that achieves a quasi uniform gain distribution. The analysis, based on a two-temperature model and the gas-transport equations, computes the electron density that supports a flat gain pattern. Combining the desired electron density with the electron-balance equations, the model determines the required electric field. The results were used to design a new set of electrodes for a home-made fast transverse flow CO 2 laser. A stable, large volume discharge ( 4 × 8 × 90 cm 3 ) with very good uniformity was obtained. The resulting gain distribution was registered in a bi-dimensional map. The peak gain rose from 1.2 m - 1 , attained with the old electrode set, to 1.6 m - 1 with the new one and the gain showed a homogeneous profile.