Email this article SECOND DEGREE LOCAL INTEGRAL FOR ROTATING SYSTEMS. PART I
- Authors: Shamshiev F.T.1
-
Affiliations:
- National University of Uzbekistan, named after Mirzo Ulugbek
- Issue: Vol 102, No 5 (2025)
- Pages: 435–446
- Section: Articles
- URL: https://journal-vniispk.ru/0004-6299/article/view/307870
- DOI: https://doi.org/10.31857/S0004629925050076
- EDN: https://elibrary.ru/PSDNGW
- ID: 307870
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Abstract
The results of a study on the existence of a quadratic local integral relative to the velocity components for stationary stellar systems in the absence of any symmetry of the gravitational potential are presented. This refers to a separate isolated invariant surface in phase space, allowing the velocity field to be determined immediately for certain specific initial conditions. All two-dimensional potentials that allow such a local integral for rotating systems are listed. In this first publication, we will limit ourselves to cases of constant energy expansion in powers and coinciding characteristics, which lead to both known and non-trivial potentials allowing a quadratic local integral. The work is partially based on a talk presented at the Modern Stellar Astronomy 2024 conference.
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About the authors
F. T. Shamshiev
National University of Uzbekistan, named after Mirzo Ulugbek
Email: shamshiyev_f@nuu.uz
Tashkent, Uzbekistan
References
- A. Clebsch (ed.), Jacobi’s Lectures on Dynamics Second Revised Edition (Amer. Mathematical Society, 2009).
- Э.Т. Уиттекер, Аналитическая динамика (Едиториал УРСС, 2004).
- A.S. Eddington, Monthly Not. Roy. Astron. Soc. 76, 37 (1915).
- G.L. Clark, Monthly Not. Roy. Astron. Soc. 97, 182 (1937).
- G.G. Kuzmin, Publ. Tartu Astrofizica Observ. 34, 457 (1964).
- P.O. Vandervoort, Astrophys. J. 232, 91 (1979).
- G. Contopoulos and P.O. Vandervoort, Astrophys. J. 389, 118 (1992).
- B. Chauvineau, Celest. Mech. Dyn. Astron. 51(4), 363 (1991).
- V.A. Antonov, Vestnik LGU 19, 97 (1981).
- D. Lynden-Bell, Monthly Not. Roy. Astron. Soc. 124, 95 (1962).
- D. Lynden-Bell, Monthly Not. Roy. Astron. Soc. 458(1), 726 (2016).
- J.S. Stodółkiewicz, Acta Astronomica 22, 375 (1972).
- J.S. Stodółkiewicz, Acta Astronomica 24, 153 (1974).
- J.S. Stodółkiewicz, Acta Astronomica 24, 265 (1974).
- J.S. Stodółkiewicz, Acta Astronomica 24, 319 (1974).
- V.A. Antonov and F.T. Shamshiev, Celest. Mech. Dyn. Astron. 56(3), 451 (1993).
- V.A. Antonov and F.T. Shamshiev, Celest. Mech. Dyn. Astron. 59, 209 (1994).
- F.T. Shamshiev, Astron. Astrophys. Trans. 7(4), 269 (1995).
- F.T. Shamshiev, J. Korean Astron. Soc. Suppl. 29, S73 (1996).
- F.T. Shamshiev, in Proc. All-Russian Conf. on Astronomy at the Epoch of Multimessenger Studies, Moscow, Russia; edited by A.M. Cherepashchuk (Moscow: Janus-K, 2022), p. 457.
- Ф.Т. Шамшиев, в сб. Тр. ин-та матем. и информ. технологий Волгоградского гос. ун-та, под ред. А.Г. Лосева, А.А. Клячина, В.А. Клячина и др. (Волгоград: Изд-во ВолГУ, 2023), p. 215.
- F.T. Shamshiev, Astrophys. Bull. 79(1), 151 (2024).
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