Email this article Regular Precession of a Gyrostat in Three Force Fields
- Authors: Ol’shanskii V.Y.1
-
Affiliations:
- IPTMU RAS
- Issue: Vol 87, No 4 (2023)
- Pages: 571-588
- Section: Articles
- URL: https://journals.rcsi.science/0032-8235/article/view/138879
- DOI: https://doi.org/10.31857/S0032823523040100
- EDN: https://elibrary.ru/MEVCBL
- ID: 138879
Cite item
Open Access
Access granted
Subscription Access
Abstract
The article gives a solution to the problem of possible conditions of regular precession in the motion of a gyrostat around a fixed point under the action of two uniform and one inhomogeneous field. For the known case with equal precession and proper rotation velocities, new solutions are indicated with the precession axis deviated from the symmetry axis of the inhomogeneous field. New cases of regular precession are found, when the ratio of precession and proper rotation velocities is equal to two or one second. Application of the results to precession in orthogonal fields and to precession of a solid are considered.
About the authors
V. Yu. Ol’shanskii
IPTMU RAS
Author for correspondence.
Email: olshanskiy_vlad@mail.ru
Russia, Saratov
References
- Bogoyavlensky O.I. Euler equations on finite dimensional Lie algebras arising in physical problems // Math. Phys. Commun., 1984, vol. 95, pp. 307–315.
- Yehia H.M. On the motion of a rigid body acted upon by potential and gyroscopic forces I. The equations of motion and their transformation // J. Theor.&Appl. Mech., 1986, vol. 5, no. 5, pp. 747–754.
- Yehia H.M. On the motion of a rigid body acted upon by potential and gyroscopic forces II. A new form of the equations of motion of a rigid body in an ideal incompressible fluid // J. Theor.&Appl. Mech., 1986, vol. 5, no. 5, pp. 755–762.
- Kharlamov M.P. Periodic motions of the Kowalevski gyrostat in two constant fields // J. Phys. A, 2008, vol. 41, iss. 27.
- Yehia H.M., El-Kenani H.N. Effect of the gravity and magnetic field to find regular precessions of a satellite-gyrostat with principal axes on a circular orbit // J. Appl. Comput. Mech., 2021, vol. 7 (4), pp. 2120–2128.
- Gorr G.V., Kovalev A.M. Motion of a Gyrostat. Kyev: Naukova Dumka, 2013. 408 p. (in Russian)
- Gorr G.V., Maznev A.V., Shchetinina E.K. Precession Motions in Rigid Body Dynamics and Dynamics of Linked Rigid Bodies Systems. Donetsk: Donetsk Nat. Univ., 2009. 222 p. (in Russian)
- Gorr G.V., Maznev A.V. Precessions of a gyrostat under the action of a potential and gyroscopic forces in the case of a variable gyrostatic momentum // Prikl. Matem. i Mekh., 2022, vol. 86, iss. 6, pp. 801–813.
- 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, iss. 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, iss. 2, pp. 216–219.
- Grioli G. Esistenza e determinazione delle prezessioni regolari dinamicamente possibili per un solido pesante asimmetrico // Ann. Mat. Pura e Appl., 1947, vol. 26, iss. 3–4, pp. 271–281.
- Ol’shanskii V.Yu. Regular precession of a rigid body in two uniform fields // Mech. Res. Commun., 2023, vol.127, art. no. 104041.
- Ol’shanskii V.Yu. Regular precession of a gyrostat in three uniform fields // Mech. Solids, 2022, vol. 57, iss. 8, pp. 1873–1884.
- Hussein A.M. Precessional motion of a rigid body acted upon by three irreducible fields // Rus. J. Nonlin. Dyn., 2019, vol. 15, iss. 3, pp. 285–292.
