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Sbornik: Mathematics, 2011, Volume 202, Issue 9, Pages 1347–1371
DOI: https://doi.org/10.1070/SM2011v202n09ABEH004190 (Mi sm7762) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Extremal trajectories and the asymptotics of the Maxwell time in the problem of the optimal rolling of a sphere on a plane

A. P. Mashtakov, Yu. L. Sachkov

Program Systems Institute of RAS
English version PDF (640 kB) Citations (11)
References:
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DOI: https://doi.org/10.1070/SM2011v202n09ABEH004190
Abstract: The problem of a sphere rolling on a plane without twisting or slipping is considered. It is required to roll the sphere from one contact configuration to another so that the length of the curve described by the contact point is minimal. A parametrization of extremal trajectories is obtained. The asymptotics of extremal trajectories and the behaviour of the Maxwell time for the rolling of a sphere over sinusoids of small amplitude are studied; for such trajectories estimates for the so-called cut time are obtained.
Bibliography: 21 titles.
Keywords: optimal control, geometric methods, symmetries of the exponential map, rolling of surfaces, Euler elastics.
Received: 24.06.2010
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 9, Pages 97–120
DOI: https://doi.org/10.4213/sm7762
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: Primary 49K15; Secondary 70B10, 93B27
Language: English
Original paper language: Russian
Citation: A. P. Mashtakov, Yu. L. Sachkov, “Extremal trajectories and the asymptotics of the Maxwell time in the problem of the optimal rolling of a sphere on a plane”, Mat. Sb., 202:9 (2011), 97–120; Sb. Math., 202:9 (2011), 1347–1371
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2011v202n09ABEH004190
  • https://www.mathnet.ru/eng/sm/v202/i9/p97
    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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