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In the present article, the rotational motion of a symmetric rigid body (gyro) about a fixed point close to Lagrange’s case is studied. This gyro is acted upon by a perturbing moment vector, a third component of a gyro moment vector, and a variable restoring moment vector. The angular velocity of the gyro is assumed to be sufficiently large, its direction is close to the axis of dynamic symmetry, and the perturbing moments are small as compared to the restoring ones. These conditions permit to introduce a small parameter. Averaged systems of the equations of motion in the first and second approximations are obtained. Also, the evolution of the precession angle up to the second approximation is determined. The graphical representations of the attained angles and its interpretations are presented.

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