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Uspekhi Mat. Nauk, 2020, Volume 75, Issue 6(456), Pages 153–161 (Mi umn9977)  

This article is cited in 1 scientific paper (total in 1 paper)

Spinning tops and magnetic orbits

S. P. Novikov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: A number of directions were initiated by the author and his students in their papers of 1981–1982. However, one of them, concerning the properties of closed orbits on the sphere $S^2$ and in the groups $S^3$ and $\operatorname{SO}_3$, has not been sufficiently developed. This paper revives the discussion of these questions, states unsolved problems, and explains what was regarded as fallacies in old papers. In general, magnetic orbits have been poorly discussed in the literature on dynamical systems and theoretical mechanics, but Grinevich has pointed out that in theoretical physics one encounters similar situations in the theory related to particle accelerators such as proton cyclotrons. It is interesting to look at Chap. III of Landau and Lifshitz's Theoretical physics, vol. 2, Field theory (translated into English as The classical theory of fields [12]), where mathematical relatives of our situations occur, but the physics is completely different and there are actual strong magnetic fields.
Bibliography: 12 titles.

Keywords: spinning tops, magnetic orbits, self-intersections.

Funding Agency Grant Number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1614
This work was performed at the Steklov International Mathematical Center and supported by the Ministry of Science and Education of Russia (agreement no. 075-15-2019-1614).


DOI: https://doi.org/10.4213/rm9977

Full text: PDF file (550 kB)
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English version:
Russian Mathematical Surveys, 2020, 75:6, 1133–1141

Bibliographic databases:

UDC: 514.853
MSC: Primary 58E05, 58E30; Secondary 49N60
Received: 28.08.2020

Citation: S. P. Novikov, “Spinning tops and magnetic orbits”, Uspekhi Mat. Nauk, 75:6(456) (2020), 153–161; Russian Math. Surveys, 75:6 (2020), 1133–1141

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Sokolov, “Non-Abelian $\mathfrak{so}_3$ Euler top”, Russian Math. Surveys, 76:1 (2021), 183–185  mathnet  crossref  crossref  mathscinet  isi  elib
  • Успехи математических наук Russian Mathematical Surveys
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