The motion of a fast spinning disc which comes out from the limiting case γ″ 0 ≈ 0

Abstract

In this paper, the problem of motion of a rigid body about a fixed point in a central Newtonian force field is studied for a singular value of the natural frequency (ω = 1) being excluded from the limiting case γ″ 0 ≈ 0 [1]. Poincaré's small parameter method [2–4] is used to investigate periodic solutions of a quasilinear autonomous system in the form of power series expansions containing assumed small parameter. Such a motion is analysed geometrically using Euler's angles to describe the orientation of the body at any instant of time. A Programm is worked out to represent the obtained analytical solutions graphically. On the other hand, the quasilinear autonomous system is solved numerically using the fourth-order Runge-Kutta method [5] and the graphical representations of such solutions are obtained through other programm. At the end part of this paper, the analytical and the numerical solutions are compared.