New cases of regular precession of an asymmetric liquid-filled rigid body

Perturbed rotations of a rigid body close to the regular precession in the Lagrangian case under the action of a restoring moment depending on slow time and nutation angle, as well as a perturbing moment slowly varying with time, are studied. The body is assumed to spin rapidly, and the restoring and perturbing moments are assumed to be small with a certain hierarchy of smallness of the components. A first approximation averaged system of equations of motion for an essentially nonlinear two-frequency system is obtained in the nonresonance case. Examples of motion of a body under the action of particular restoring, perturbing, and control moments of force are considered.

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Regular precession of a rigid body (gyrostat) acted upon by an irreducible combination of three classical fields

Journal of the Egyptian Mathematical Society ◽

10.1016/j.joems.2016.08.001 ◽

2017 ◽

Vol 25 (2) ◽

pp. 216-219 ◽

Cited By ~ 3

Author(s):

H.M. Yehia

Keyword(s):

Rigid Body ◽

Regular Precession ◽

Classical Fields

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New Treatment of the Rotary Motion of a Rigid Body with Estimated Natural Frequency

Advances in Astronomy ◽

10.1155/2020/6629183 ◽

2020 ◽

Vol 2020 ◽

pp. 1-12

Author(s):

A. I. Ismail

Keyword(s):

Rigid Body ◽

Natural Frequency ◽

Numerical Solutions ◽

Equations Of Motion ◽

Geometric Interpretation ◽

Parameter Method ◽

Large Parameter ◽

Regular Precession ◽

New Treatment ◽

The Stability

In this paper, the problem of the motion of a rigid body about a fixed point under the action of a Newtonian force field is studied when the natural frequency ω = 0.5 . This case of singularity appears in the previous works and deals with different bodies which are classified according to the moments of inertia. Using the large parameter method, the periodic solutions for the equations of motion of this problem are obtained in terms of a large parameter, which will be defined later. The geometric interpretation of the considered motion will be given in terms of Euler’s angles. The numerical solutions for the system of equations of motion are obtained by one of the well-known numerical methods. The comparison between the obtained numerical solutions and analytical ones is carried out to show the errors between them and to prove the accuracy of both used techniques. In the end, we obtain the case of the regular precession type as a special case. The stability of the motion is considered by the phase diagram procedures.

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