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This work outlines the motion of a disc about one of its fixed point different from its center of mass in the presence of a constant gyrostatic moment about the principal axes of inertia. The governing system of motion consists of six nonlinear differential equations and their first integrals are reduced to another quasilinear autonomous one of 2DOF besides one first integral. Initially, it is hypothesized that the body is rapidly spun about one of its principal axes. The method of small parameter of Poincaré is used to achieve the desired approximate solutions of the equations of motion. Euler's angles are used to interpret the motion of the body at any blink. The numerical solutions of autonomous system are investigated using the fourth order Runge-Kutta algorithms (RKA). The comparison between both two solutions reveals that the numerical solutions are in well agreement with the approximate ones and the deviation between them is very slightly. The importance of this work is focused on its great applications in many fields such as in engineering, physics and industrial applications for example ships stabilizers, racing cars, pointing devices for computer, satellites and like.

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