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One Class of Resonance Precession Motions of a Rigid Body under the Action of Three Homogeneous Force Fields
- Authors: Gorr G.V.1
-
Affiliations:
- State Budgetary Institution “Institute of Applied Mathematics and Mechanics”
- Issue: Vol 87, No 1 (2023)
- Pages: 3-18
- Section: Articles
- URL: https://rjonco.com/0032-8235/article/view/675181
- DOI: https://doi.org/10.31857/S0032823523010071
- EDN: https://elibrary.ru/HVLUQK
- ID: 675181
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Abstract
The article is devoted to the problem on motion of a rigid body with a fixed point under the action of a force field, which is the superposition of three homogeneous force fields. Existence conditions are investigated for precession motions, which are characterized by the following property: the angular velocity of the precession of the body is two times more than the angular velocity of its proper rotation. It is established that the body has the dynamic symmetry with respect to an axis making a constant angle with a vector fixed in the immovable space. In the case of the body with the spherical mass distribution this angle equals to \({\text{arccos}}\frac{1}{4}\). Solution of the equations of motion of the body is expressed through the elliptic functions of time.
About the authors
G. V. Gorr
State Budgetary Institution “Institute of Applied Mathematics and Mechanics”
Author for correspondence.
Email: gvgorr@gmail.com
Russia, Donetsk
References
- Ishlinskii A.Yu. Orientation, Gyroscopes and Inertial Navigation. Moscow: Nauka, 1976. 672 p. (in Russian)
- Klein F., Sommerfeld A. Über die Theorie des Kreisels. N.Y.: Johnson Reprint Corp., 1965. 966 p.
- Grioli G. Esistenza e determinazione delle precessioni regolari dinamicamente possibili per un solido pesante asimmetrico // Ann. Math. Pura et Appl., 1947, ser. 4, vol. 26, fasc. 3–4. P. 271–281.
- Gorr G.V. Precession motions in the rigid body dynamics and in the dynamics of coupled rigid bodies systems // JAMM, 2003, vol. 67, no. 4, pp. 573–587. (in Russian)
- Bressan A. Sulle precessioni d’un corpo rigido costituenti moti di Hess // Rend. Semin. Mat. Univ. Padova, 1957, vol. 27, pp. 276–283.
- Dokshevich A.I. Finite Form Solutions of Euler–Poisson Equations. Kiev: Nauk. Dumka, 1992. 168 p. (in Russian)
- Gorr G.V., Maznev A.V., Shchetinina E.K. Precession Motions in the Rigid Body Dynamics and in the Dynamics of Coupled Rigid Bodies. Donetsk: Donetsk National Univ., 2009. 222 p. (in Russian)
- Gorr G.V., Maznev A.V. Dynamics of a Gyrostat Having a Fixed Point. Donetsk: Donetsk National Univ., 2010. 364 p. (in Russian)
- Gorr G.V., Maznev A.V. Motion of a Gyrostat with the Variable Gyrostatic Moment. Donetsk: Inst. of Appl. Math. Mech., 2017. 250 p. (in Russian)
- Gorr G.V., Rubanovskii V.N. On one new class of motions of a system of rigid bodies coupled by hinges // JAMM, 1988, vol. 50, no. 5, pp. 707–712. (in Russian)
- Ol’shanskii V.Yu. On regular precessions of an asymmetrical rigid body with the liquid filling // JAMM, 2018, vol. 82, no. 5, pp. 559–571. (in Russian)
- Ol’shanskii V.Yu. New cases of regular precession of an asymmetrical liquid-filled rigid body // Celest. Mech. Dyn. Astron., 2019, vol. 131, no. 12, art. no. 57.
- Ol’shanskii V.Yu. Analysis of regular precession conditions for asymmetrical liquid-filled rigid body // Celest. Mech. Dyn. Astron., 2020, vol. 132, no. 9, art. no. 46.
- Ol’shanskii V.Yu. Semi-regular precession of an asymmetrical rigid body with the liquid filling // JAMM, 2021, vol. 85, no. 5, pp. 547–564. (in Russian)
- Yehia H.M. On the regular precession of an asymmetric rigid body acted upon by uniform gravity and magnetic fields // Egypt. J. Bas. Appl. Sci., 2015, vol. 2, no. 3, pp. 200–205.
- Yehia H.M. Regular precession of a rigid body (gyrostat) acted upon by an irreducible combination of three classical fields // J. Egypt. Math. Soc., 2017, vol. 25, no. 2, pp. 216–219.
- Hessein A.M. Precessional motion of a rigid body acted upon by three irreducible fields // Rus. J. Nonlin. Dyn., 2019, vol. 15, no. 3, pp. 285–292.
- Maznev A.V. Precessional-isoconical motions in one solution of Kirchhoff equations // Bull. Donetsk Univ., Ser. A: Nature Sci., 2021, no. 2, pp. 12–16. (in Russian)
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