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.
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
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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
\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
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\crossref{https://doi.org/10.1134/S1560354713040047}
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https://www.mathnet.ru/eng/rcd118
https://www.mathnet.ru/eng/rcd/v18/i4/p372
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Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “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
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
E. J. Haug, “An ordinary differential equation formulation for multibody dynamics: nonholonomic constraints”, J. Comput. Inf. Sci. Eng., 17:1 (2017), 011009
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I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Hamiltonization of elementary nonholonomic systems”, Russ. J. Math. Phys., 22:4 (2015), 444–453
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
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