Stability and Instability of an Earth Satellite with a Cylindrical Shield in the Newtonian Central Force Field for Accuracy

Abstract

The stability and instability of motion of an artificial Earth satellite equipped with a cylindrical electrostatic shield in a circular equatorial orbit is studied. The satellite traveling through the Earth's magnetic field causes Lorentz forces. For the sake of accuracy, the second-order terms of R^-1are retained for the potential function of the Newtonian central force field. The Lorentz forces and Newtonian central force field have an effect on the stability and instability affect the conditions. Right equilibrium positions of the satellite in the orbital coordinate system are considered. Furthermore, we study the stability of motion when the axisymmetric shielded satellite rotates at an arbitrary speeds in a circular orbit under the influence of gravitational forces and Lorentz forces. Finally, as the numerical examples show, the stable results present periodic oscillation about the zero solutions. The Lorentz forces lead to low frequency in the system, the third mass moment in the Newtonian central force field becomes more accurate, and the cumulative effect is considerable.