In the present work, the problem of the dynamical motion of a rigid body close to Lagrange’s gyroscope under the effectiveness of a gyro moment vector, perturbing moments, and a Newtonian field is examined. An averaging system of the governing equations of motion is gained in view of applying the averaging method. A case of linear dissipative moments is considered. The numerical solutions for the case of linear dissipative moments are achieved and represented in some plots to detect the well effect of the different parameters on the motion of the body. The prominence of this work is due to its great applications in physics and engineering industry. Keywords: Gyroscopic motion, Euler's dynamic equations, Euler's angles, Newtonian field, Perturbation methods