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The fast spinning motion of a rigid body in the presence of a gyrostatic momentum ℓ3

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Summary

In this paper, the rotational motion of a rigid body about a fixed point in the Newtonian force field [1] with a gyrostatic momentum ℓ3 about thez-axis is considered. The equations of motion and their first integrals are obtained and reduced to a quasi-linear autonomous system with two degrees of freedom with one first integral. Poincaré's small parameter method [2] is applied to investigate the analytical periodic solutions of the equations of motion of the body with one point fixed, rapidly spinning about one of the principal axes of the ellipsoid of inertia. A geometric interpretation of motion is given by using Euler's angles [3] to describe the orientation of the body at any instant of time.

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References

  1. El-Barki, F. A., Ismail, A. I.: Limiting case for the motion of a rigid body about a fixed point in the Newtonian force field. ZAMM75, 821–829 (1995).

    Google Scholar 

  2. Malkin, I. G.: Some problems in the theory of nonlinear oscillations. United States Atomic Energy Commission. Technical Information Service, ABC-tr-3766, 1959.

  3. Ismail, A. I.: Treating a singular case for a motion of a rigid body in a Newtonian field of force. Arch. Mech.49, 1091–1101 (1997).

    Google Scholar 

  4. Arkhangel'skii, Iu. A.: On the algebraic integrals in the problem of motion of a rigid body in a Newtonian field of force. PMM27, 171–175 (1963).

    Google Scholar 

  5. Arkhangel'skii, Iu. A.: On a motion of an equilibrated gyroscope in the Newtonian force field. PMM27, 1099–1101 (1963).

    Google Scholar 

  6. Sedunova, S. P.: Some motions of a heavy rigid body about a fixed point. Dynamics of machines and working processes. Chelyabinsk Polytechn. Inst., vol. 129 (1973).

  7. Arkhangel'skii, Iu. A.: On a motion about a fixed point of a fast spinning heavy solid. PMM27, 864–877 (1963).

    Google Scholar 

  8. Ismail, A. I.: The motion of fast spinning rigid body about a fixed point with definite natural frequency. Aerospace Sci. Technol.3, 183–190 (1997).

    Google Scholar 

  9. Ismail, A. I.: On the application of Krylov-Bogoliubov-Mitropolski technique for treating the motion about a fixed point of a fast spinning heavy solid. ZFW20, 205–208 (1996).

    Google Scholar 

  10. Arhangel'skii, Iu. A.: Construction of periodic solutions for the Euler-Poisson equations by means of power series expansion containing a small parameter. Colloquia Mathematica Societatis Janos Bolyai, Keszthely (Hungary), 1975.

  11. Ismail, A. I.: The motion of a fast spinning disc which comes out from the limiting case γ0″≈0. Comp. Methods Appl. Mech. Engng161, 67–76 (1998).

    Google Scholar 

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Ismail, A.I., Amer, T.S. The fast spinning motion of a rigid body in the presence of a gyrostatic momentum ℓ3 . Acta Mechanica 154, 31–46 (2002). https://doi.org/10.1007/BF01170697

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  • DOI: https://doi.org/10.1007/BF01170697

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