This study investigates the 3D motion of a rigid body (RB) rotating around a fixed point, focusing on Lagrange's case while considering the effects of a gyrostatic moment (GM) and a Newtonian force field (NFF). It is notably that the center of mass is displaced very much from the principal dynamic symmetry axis. Utilizing the fundamental principle of angular momentum, the equations of motion (EOM) are formulated and solved applying the large parameter approach (LPA) to determine approximate solutions (AS) for the irrational frequencies' case. Euler's angles, which define the body's orientation at any moment, are explicitly calculated. Additionally, to assess the impact of applied moments on motion stability, we utilize advanced computational tools to generate graphical representations of the achieved solutions and the related Euler's angles. This work enhances the understanding of RB dynamics in complex motion scenarios, emphasizing the interaction between external forces and GMs in shaping stability and behavior. The study is poised to greatly influence the aerospace industry by advancing our understanding of rotational motion and the dynamics of celestial bodies, with direct applications in the design and operation of spaceships, spacecraft, and satellites.
Amer et al. (Sat,) studied this question.