Email this article 
Kovalevskaya top and attitude dynamics of magnetized satellites in equatorial orbits
- Authors: Doroshin A.V.1, Aslanov V.S.1
-
Affiliations:
- Samara National Research University
- Issue: Vol 89, No 3 (2025)
- Pages: 369-384
- Section: Articles
- URL: https://ogarev-online.ru/0032-8235/article/view/306479
- DOI: https://doi.org/10.31857/S0032823525030012
- EDN: https://elibrary.ru/jkbrrr
- ID: 306479
Cite item
Open Access
Access granted
Subscription Access
Abstract
The article gives a visual illustration of the dynamics of a heavy rigid body around a fixed point in the case of S.V. Kovalevskaya, which arises in the framework of applied problems of space flight. The motion of a rigid body in the case of S.V. Kovalevskaya (the Kovalevskaya top) is equivalent to the dynamics of the attitude of a magnetized satellite around its centre of mass during orbital motion along equatorial circular orbits. The perturbed motion of the magnetized satellite is considered at small deviations from the conditions of the Kovalevskay top, including a small dynamic asymmetry of the satellite, as well as small variations in the magnitude of the external magnetic moment due to weak ellipticity or non-equatoriality of the orbits.
About the authors
A. V. Doroshin
Samara National Research University
Author for correspondence.
Email: doran@inbox.ru
Samara, Russia
V. S. Aslanov
Samara National Research University
Email: aslanov_vs@mail.ru
Samara, Russia
References
- Sophie Kowalevski.Sur le probleme de la rotation d'un corps solide autour d'un point fixe // Acta Math., 1889, vol. 12, pp. 177–232.
- Golubev V.V.Lectures on Integrating Equations of Motion of a Heavy Rigid Body around a Fixed Point. Moscow;Leningrad: Gostekhizdat, 1953. 287 p. (in Russian)
- Arkhangelsky Yu.A.1977 Analytical Dynamics of a Rigid Body. Moscow: Nauka, 1977. 328 p. (in Russian)
- Kozlov V.V.Dynamic systems arising on the invariant tori of the Kowalewska problem // JAMM, 1975, vol. 39, no. 1, pp. 20–25.
- Veselov A.P., Novikov S.P.Poisson brackets and complex tori // Tr. Mat. Inst. Steklov, 1984, vol. 165, pp. 49–61.
- Reiman A.G., Semenov-Tyan-Shanskii M.A.Lax representation with a spectral parameter for thekowalevski top and its generalizations // Funct. Anal& Its Appl., 1988, vol. 22, no. 2, pp. 158–160.
- Kharlamov M.P.Bifurcation of common levels of first integrals of the Kovalevskaya problem // JAMM, 1983, vol. 47, no. 6, pp. 737–743.
- Dullin H.R., Juhnke M., Richter P.H.Action integrals and energy surfaces of the Kovalevskaya top // Int. J. of Bifurc.&Chaos, 1994, vol. 4, no. 06, pp. 1535–1562.
- Komarov I.V.A generalization of the Kovalevskaya top // Phys. Lett., 1987, vol. 123, no. 1, pp. 14–15.
- Yehia H.New integrable cases in the dynamics of rigid bodies // Mech. Res. Commun., 1986, vol. 13, no. 3, pp. 169–172.
- Bogoyavlenskii O.I.Integrable Euler equations on Lie algebras arising in problems of mathematical physics // Izv. RAN. Ser. Matem., 1984, vol. 48, no. 5, pp. 883–938.
- Doroshin A.V.Homoclinic solutions and motion chaotization in attitude dynamics of a multi-spin spacecraft // Commun. in Nonlin. Sci.&Numer. Simul., 2014, vol. 19, no. 7, pp. 2528–2552.
- Richter P.H., Dullin H.R., Wittek A.Kovalevskaya top // Publ. Wiss. Film. Tech. Wiss. /Naturw, 1997, vol. 13, pp. 33–96.
- Borisov A.V., Mamaev I.S.Rigid Body Dynamics.v. 52. Walter de Gruyter GmbH&Co KG, 2018. 521 p.
Supplementary files
