Symbolic-Numerical Investigation of Gyrostat Satellite Dynamics

Dynamics of gyrostat satellite moving along a circular orbit in the central Newtonian gravitational field is studied. A symbolicnumerical method for determination of all equilibrium orientations of gyrostat satellite in the orbital coordinate system with given gyrostatic torque and given principal central moments of inertia is proposed. A computer algebra method based on the algorithm for the construction of a Groebner basis and the resultant concept for solving the problem is used. All bifurcation values of parameters at which there is a change of numbers of equilibrium orientations are determined. Evolution of domains in the space of parameters of the system which correspond to various numbers of equilibria are carried out numerically in detail. The stability analysis of equilibria is performed on the basis of Lyapunov’s theorem. It is shown that the number of equilibria of the gyrostat satellite in general case is no less than 8 and no more than 24, and the number of stable equilibria changes from 4 to 2.