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Sbornik: Mathematics, 2016, Volume 207, Issue 7, Pages 915–941
DOI: https://doi.org/10.1070/SM8555 (Mi sm8555) 		 
This article is cited in 8 scientific papers (total in 8 papers)

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
English version PDF (1357 kB) Citations (8)
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DOI: https://doi.org/10.1070/SM8555
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.
Received: 08.06.2015 and 04.04.2016
Russian version:
Matematicheskii Sbornik, 2016, Volume 207, Number 7, Pages 29–56
DOI: https://doi.org/10.4213/sm8555
Bibliographic databases:
Document Type: Article
UDC: 517.538
MSC: Primary 53C17; Secondary 49J15
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:125
    English version PDF:15
    References:72
    First page:64
     
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