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Mat. Sb., 2016, Volume 207, Number 7, Pages 29–56 (Mi msb8555)  

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

Geodesics in the sub-Riemannian problem on the group $\mathrm{SO}(3)$

I. Yu. Beschastnyi, Yu. L. Sachkov

Ailamazyan Program Systems Institute of Russian Academy of Sciences, Yaroslavskaya obl., Pereslavskii raion, s. Ves'kovo

Abstract: Geodesics of left-invariant sub-Riemannian structures are considered on the group $\mathrm{SO}(3)$. A complete description of periodic geodesics, their elementary properties, certain necessary conditions for minimality and estimates for the cut time and the diameter of the metric are presented.
Bibliography: 32 titles.

Keywords: sub-Riemannian geometry, almost Riemannian geometry, optimal control, geodesic curves, cut time.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8555

Full text: PDF file (1396 kB)
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English version:
Sbornik: Mathematics, 2016, 207:7, 915–941

Bibliographic databases:

UDC: 517.538
MSC: Primary 53C17; Secondary 49J15
Received: 08.06.2015 and 04.04.2016

Citation: I. Yu. Beschastnyi, Yu. L. Sachkov, “Geodesics in the sub-Riemannian problem on the group $\mathrm{SO}(3)$”, Mat. Sb., 207:7 (2016), 29–56; Sb. Math., 207:7 (2016), 915–941

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. Bolsinov A. Bao J., “A Note About Integrable Systems on Low-Dimensional Lie Groups and Lie Algebras”, Regul. Chaotic Dyn., 24:3 (2019), 266–280  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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