Abstract: In the present work, we investigate the perturbed
rotational motions of a symmetric rigid body (gyrostat) about a fixed point,
which are close to Lagrange’s case. This gyrostat is acted upon by a
gyrostatic moment vector whose
components act on the moving axes x, y
and z; restoring moment k and
perturbing moment vector The moment k
is introduced to express the rotation of the body under the action of uniform
magnetic field of strength and a point
charge e located on the axis of
symmetry. It is assumed that the angular velocity is large, its direction is
close to the axis of dynamic symmetry of the body and that two projections of
the perturbing moment vector onto the principal axes of inertia of the body are
small as compared to the restoring moment k
while the third one is of the same order as it. A small parameter is introduced
in a special way and the averaging method is used to obtain the first order
approximate solutions of the equations of motion. A theoretical description for
this approach in the resonant and non-resonant cases is given.
Keywords and phrases: Euler’s equations, rigid body, averaging method.
