The 3D modeling analysis for the rotary motion of an asymmetric rigid body (RB) that gains a charge is presented. Under the effect of a gyrostatic moment (GM), an electromagnetic force field (EFF), time-varying body-fixed torques (TVBFTs), and constant axial torque (CAT), Euler’s equation of motion (EOM) is derived to describe the body’s EOM. The process is to derive the analytic solutions for the general attitude motion of the RB that is nearly symmetrical; therefore, a novel analytical solution for the angular velocities of the body has been approached. These new solutions are obtained by considering torques that vary over time and expressing them as integrals. Additionally, a novel closed-form evaluation mechanism for these integrals is offered. Specifically, the case of a constant torque around the spin axis and transverse torques represented by polynomial functions of time is explored. When dealing with an axisymmetric RB subject to a CAT, the solutions obtained from Euler’s EOM are exact. However, it is important to note that novel analytic solutions for the Eulerian angles are approximations, as they rely on the assumption of small angles. Nonetheless, these approximations have broad applicability to a wide range of practical problems. The method’s precision is demonstrated through the graphical simulation of the proposed solutions. Additionally, a computer program is utilized to create diagrams and phase plane curves, highlighting the contribution of various body parameters to the motion. These plots depict the contributions of various values regarding GM, charge, and CAT. Motion stability is also examined through phase diagrams. In addition to presenting novel solutions and outcomes for the problem, this study plays a vital role in multiple scientific and engineering fields as it has the potential to optimize mechanical systems, explain celestial motion, and improve spacecraft performance.
