THE MOTION OF FAST SPINNING RIGID-BODY ABOUT A FIXED-POINT WITH DEFINITE NATURAL FREQUENCY

In this paper, the problem of motion of a rigid body about a fixed poi nt under the action of a Newtonian force field is studied when the nat ural frequency value omega = 1/3. This singularity appears in [1] and deals with different bodies being classified according to the moments of inertia. Using Poincare's small parameter method [2], periodic solu tions - with zero basic amplitudes - of the quasilinear autonomous sys tem are obtained in the form of power series expansions, up to the thi rd approximation, containing assumed small parameter. Also, Lagrange's gyroscope and Euler's one are derived as special cases from our solut ions. At the end, the geometric interpretation of motion using Euler's angles is considered to show that the resulted motion is of regular p recession type which depends on four arbitrary constants.