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Regul. Chaotic Dyn., 2013, Volume 18, Issue 4, Pages 372–379 (Mi rcd118)  

This article is cited in 6 scientific papers (total in 6 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

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.


DOI: https://doi.org/10.1134/S1560354713040047

References: PDF file   HTML file

Bibliographic databases:

Received: 19.06.2013
Accepted:30.06.2013
Language:

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://www.ams.org/mathscinet-getitem?mr=3090207}
\zmath{https://zbmath.org/?q=an:1338.37033}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000322878100004}


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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. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Dynamics and Control of an Omniwheel Vehicle”, Regul. Chaotic Dyn., 20:2 (2015), 153–172  mathnet  crossref  mathscinet  zmath  adsnasa
    2. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Hamiltonization of elementary nonholonomic systems”, Russ. J. Math. Phys., 22:4 (2015), 444–453  crossref  mathscinet  zmath  isi  scopus
    3. Yu. N. Fedorov, L. C. Garcia-Naranjo, J. C. Marrero, “Unimodularity and preservation of volumes in nonholonomic mechanics”, J. Nonlinear Sci., 25:1 (2015), 203–246  crossref  mathscinet  zmath  isi  scopus
    4. I. A. Bizyaev, “Invariantnaya mera v zadache o kachenii diska po ploskosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:4 (2017), 576–582  mathnet  crossref  elib
    5. E. J. Haug, “An ordinary differential equation formulation for multibody dynamics: nonholonomic constraints”, J. Comput. Inf. Sci. Eng., 17:1 (2017), 011009  crossref  isi  scopus
    6. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “An Invariant Measure and the Probability of a Fall in the Problem of an Inhomogeneous Disk Rolling on a Plane”, Regul. Chaotic Dyn., 23:6 (2018), 665–684  mathnet  crossref  mathscinet
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