A problem of the gyroscopic motions around a fixed point, under the action of a gyrostatic moment vector, in presence of electromagnetic field and Newtonian one, is considered. The small parameter technique is used to investigate the periodic solutions for the derived equations of such motion problem. A geometric interpretation of motion will be given in terms of Euler’s angles (θ, ψ, ϕ). Computer programs are carried out to integrate the attained quasilinear autonomous system using a fourth‐order Runge‐Kutta method. A comparison between the obtained analytical solutions and the numerical ones is investigated to calculate the errors between them.