Optimal parameters of a gravitational system satellite-stabilizer

Dynamics of a gravitational system satellite-stabilizer is studied. It is assumed that there exists viscous friction in the hinge connecting the system components but there is no spring resistance. The plane motion in a circular orbit is analyzed; the parameters that provide the most rapid damping of the natural oscillations in the vicinity of the equilibrium are determined. To estimate the duration of the transitional processes, the degree of stability of the linearized equations of motion is used. As a result of optimization with respect to dimensionless damping coefficient, the space of the system's parameters is divided into several domains. In each of these domains, the maximum degree of stability takes place on a specific configuration of characteristic equation roots. It is shown that the global optimum is achieved in the two points of the parameter space. Here one of the system’s bodies degenerates into a plate, and the characteristic equation has four equal real roots.