| Abstract | Understanding how satellites move and interact with celestial bodies involves solving tough math problems, which often need cutting-edge analytical tools to get workable results. In this study, the three-dimensional rotating movement of a charged satellite in a Newtonian field around a fixed point with the gyrostatic moment taken into account is thoroughly examined in this study. It has been proposed that the center of mass of the satellite is slightly far from the axis of symmetry. Using Euler-Poisson equations, the governing nonlinear differential equations of the motion and their first integrals are obtained. The nondimensional forms of these equations are obtained. For irrational frequency scenarios, the small parameter technique of Poincaré is employed to provide the novel approximate solutions for both Euler and Poisson equations. Additionally, the equations for Euler angles that define the satellite’s orientation at each given time are obtained and solved with the same approach. The influence of various torques and fields on the satellite motion is investigated as the angular velocity and Euler angles solutions are illustrated graphically to show how the gyrostatic moment, electromagnetic, and Newtonian fields affect both motion and stability. Controlling these parameters will be essential in maintaining and controlling the orientation of the satellite stabilization. A comparison between this study and recent ones has been made to stand on the novelty of these outcomes. The methods developed in this work have a wide range of applications in industry, including defining the motion of three-dimensional frames of robots and in carriages, airplanes, rockets, and spacecraft. This study demonstrates how the mathematical framework helps engineers predict and control satellite behavior in realistic space environments where perfect symmetry and neutral charge are rarely achieved. |