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This work demonstrates the 3D motion of 6-DOF rigid body around the main inertial axes relative to a fixed point. The novelty of this work is to examine the influence of the gyrostatic moment vector and the magnetic field on the gyrostatic motion besides the action of the Newtonian field in accordance with the Bobylev-Steklov conditions. This motion is characterized by the possibility of placing an acceptable constraint on the governing system of motion in the form of imposing a large value of the projection of the angular velocity around the axial axis of the body. The importance of this restriction is that the governing system in addition to the first-integrals can be reduced to an appropriate system of two semi-linear differential equations from second-order and one first integral. The new analytic approximate solutions of the governing equations are achieved using the small parameter technique of Poincaré. Euler’s angles are determined to evaluate the motion at any instance. The realized solutions are represented graphically for different values of the gyrostatic moment and the point charge causing the magnetic field to estimate the impact of these values on the rotational motion. Moreover, the phase plane plots which illustrate the stability behavior of the body are portrayed. The significance of this work goes back to its several applications in practical life and in engineering application like satellites, submarines, and aircraft.
He et al. (Fri,) studied this question.