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Sbornik: Mathematics, 2010, Volume 201, Issue 7, Pages 1029–1051
DOI: https://doi.org/10.1070/SM2010v201n07ABEH004101
(Mi sm7617)
 

This article is cited in 16 scientific papers (total in 16 papers)

Maxwell strata and symmetries in the problem of optimal rolling of a sphere over a plane

Yu. L. Sachkov

Program Systems Institute of RAS
References:
Abstract: The problem of rolling of a sphere over a plane without slipping or twisting is considered. It is required to roll the sphere from one contact configuration into another one so that the curve traced by the contact point be of minimum length. Extremal trajectories in this problem were described by Arthur, Walsh and Jurdjevic.
In this work, discrete and continuous symmetries of the problem are constructed and fixed points of the action of these symmetries in the inverse image and image of the exponential map are studied. This analysis is used to derive necessary conditions for optimality; namely, upper bounds on the cut time along the extremal trajectories.
Bibliography: 21 titles.
Keywords: optimal control, geometric methods, symmetries, rolling of surfaces, Euler elastica.
Received: 04.08.2009 and 03.03.2010
Russian version:
Matematicheskii Sbornik, 2010, Volume 201, Number 7, Pages 99–120
DOI: https://doi.org/10.4213/sm7617
Bibliographic databases:
Document Type: Article
UDC: 517.977.52
MSC: Primary 70E15; Secondary 53C17, 93B29
Language: English
Original paper language: Russian
Citation: Yu. L. Sachkov, “Maxwell strata and symmetries in the problem of optimal rolling of a sphere over a plane”, Sb. Math., 201:7 (2010), 1029–1051
Citation in format AMSBIB
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\by Yu.~L.~Sachkov
\paper Maxwell strata and symmetries in the problem of optimal rolling of a~sphere over a~plane
\jour Sb. Math.
\yr 2010
\vol 201
\issue 7
\pages 1029--1051
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Linking options:
  • https://www.mathnet.ru/eng/sm7617
  • https://doi.org/10.1070/SM2010v201n07ABEH004101
  • https://www.mathnet.ru/eng/sm/v201/i7/p99
  • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:690
    Russian version PDF:265
    English version PDF:20
    References:100
    First page:12
     
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