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Regular and Chaotic Dynamics, 2013, Volume 18, Issue 4, Pages 372–379
DOI: https://doi.org/10.1134/S1560354713040047 (Mi rcd118) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Non-Existence of an Invariant Measure for a Homogeneous Ellipsoid Rolling on the Plane

Luis C. García-Naranjoa, Juan C. Marrerob

a Departamento de Matemáticas y Mecánica, IIMAS-UNAM Apdo Postal 20-726, Mexico City, 01000, Mexico
b ULL-CSIC Geometría Diferencial y Mecánica Geométrica Departamento de Matemática Fundamental, Facultad de Matemáticas, Universidad de La Laguna, La Laguna, Tenerife, Canary Islands, Spain
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DOI: https://doi.org/10.1134/S1560354713040047
Abstract: It is known that the reduced equations for an axially symmetric homogeneous ellipsoid that rolls without slipping on the plane possess a smooth invariant measure. We show that such an invariant measure does not exist in the case when all of the semi-axes of the ellipsoid have different length.
Keywords: nonholonomic mechanical systems, invariant volume forms, symmetries, reduction.
Funding agency Grant number
Ministerio de Educación y Ciencia, Spain MTM2009-13383
MTM2011-15725-E
MTM2012-34478
Project of the Canary Government ProdID20100210
This work has been partially supported by MEC (Spain) Grants MTM2009-13383, MTM2011-15725-E, MTM2012-34478 and the project of the Canary Government ProdID20100210.
Received: 19.06.2013
Accepted: 30.06.2013
Bibliographic databases:
Document Type: Article
Language: English
Citation: Luis C. García-Naranjo, Juan C. Marrero, “Non-Existence of an Invariant Measure for a Homogeneous Ellipsoid Rolling on the Plane”, Regul. Chaotic Dyn., 18:4 (2013), 372–379
Citation in format AMSBIB
\Bibitem{GarMar13}
\by Luis C. Garc{\'\i}a-Naranjo, Juan C. Marrero
\paper Non-Existence of an Invariant Measure for a Homogeneous Ellipsoid Rolling on the Plane
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 4
\pages 372--379
\mathnet{http://mi.mathnet.ru/rcd118}
\crossref{https://doi.org/10.1134/S1560354713040047}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3090207}
\zmath{https://zbmath.org/?q=an:1338.37033}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000322878100004}
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  • https://www.mathnet.ru/eng/rcd/v18/i4/p372
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:40
     
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