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Regul. Chaotic Dyn., 2017, Volume 22, Issue 3, Pages 239–247 (Mi rcd254)  

This article is cited in 7 scientific papers (total in 7 papers)

The Inertial Motion of a Roller Racer

Ivan A. Bizyaev

Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: This paper addresses the problem of the inertial motion of a roller racer, which reduces to investigating a dynamical system on a (two-dimensional) torus and to classifying singular points on it. It is shown that the motion of the roller racer in absolute space is asymptotic. A restriction on the system parameters in which this motion is bounded (compact) is presented.

Keywords: roller racer, invariant measure, nonholonomic mechanics, scattering map.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation (project 14-50-00005).


DOI: https://doi.org/10.1134/S1560354717030042

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 37J60, 37C10
Received: 29.03.2017
Accepted:27.04.2017
Language: English

Citation: Ivan A. Bizyaev, “The Inertial Motion of a Roller Racer”, Regul. Chaotic Dyn., 22:3 (2017), 239–247

Citation in format AMSBIB
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\by Ivan A. Bizyaev
\paper The Inertial Motion of a {\it Roller Racer}
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 3
\pages 239--247
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\crossref{https://doi.org/10.1134/S1560354717030042}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3658423}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85020165692}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Borisov, I. S. Mamaev, “Neodnorodnye sani Chaplygina”, Nelineinaya dinam., 13:4 (2017), 625–639  mathnet  crossref  elib
    2. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration”, Regul. Chaotic Dyn., 22:8 (2017), 955–975  mathnet  crossref
    4. Alexey V. Borisov, Ivan S. Mamaev, “An Inhomogeneous Chaplygin Sleigh”, Regul. Chaotic Dyn., 22:4 (2017), 435–447  mathnet  crossref  mathscinet
    5. Ivanov A.P., “On Singular Points of Equations of Mechanics”, Dokl. Math., 97:2 (2018), 167–169  crossref  zmath  isi  scopus
    6. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Exotic Dynamics of Nonholonomic Roller Racer with Periodic Control”, Regul. Chaotic Dyn., 23:7-8 (2018), 983–994  mathnet  crossref
    7. Vitaliy Fedonyuk, Phanindra Tallapragada, “The Dynamics of a Chaplygin Sleigh with an Elastic Internal Rotor”, Regul. Chaotic Dyn., 24:1 (2019), 114–126  mathnet  crossref
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