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.
A slowly rotating coil system for AC field measurements of Fermilab Booster correctors
A method for measurement of rapidly changing magnetic fields has been developed and applied to the testing of new room temperature corrector packages designed for the Fermilab Booster Synchrotron. The method is based on fast digitization of a slowly rotating tangential coil probe, with analysis combining the measured coil voltages across a set of successive magnet current cycles. This paper presents results on the field quality measured for the normal and skew dipole, quadrupole, and sextupole elements in several of these corrector packages.