The Motion of a Rigid Body with Irrational Natural Frequency

الملخص EN

In this paper, we consider the problem of the rotational motion of a rigid body with an irrational value of the frequency ω.

The equations of motion are derived and reduced to a quasilinear autonomous system.

Such system is reduced to a generating one.

We assume a large parameter μ proportional inversely with a sufficiently small component ro of the angular velocity which is assumed around the major or the minor axis of the ellipsoid of inertia.

Then, the large parameter technique is used to construct the periodic solutions for such cases.

The geometric interpretation of the motion is obtained to describe the orientation of the body in terms of Euler’s angles.

Using the digital fourth-order Runge-Kutta method, we determine the digital solutions of the obtained system.

The phase diagram procedure is applied to study the stability of the attained solutions.

A comparison between the considered numerical and analytical solutions is introduced to show the validity of the presented techniques and solutions.