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UFN, 2015, Volume 185, Number 12, Pages 1342–1344 (Mi ufn5440)  

This article is cited in 5 scientific papers (total in 5 papers)

LETTERS TO THE EDITORS

On the validity of the nonholonomic model of the rattleback

S. P. Kuznetsovab

a Udmurt State University, Izhevsk
b Saratov Branch, Kotel'nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences

Abstract: In connection with the problem of a convex-shaped solid body on a rough horizontal plane (the rattleback or Celtic stone), the paper discusses the validity of the nonholonomic model which postulates that the contact point has zero velocity and, hence, friction performs no mechanical work. While abstract, this model is undoubtedly constructive, similar to many idealizations commonly used in science. Despite its energy-conserving nature, the model does not obey Liouville's theorem on phase volume conservation, thus allowing the occurrence in the phase space of objects characteristic of dissipative dynamics (attractors) and thereby leading to phenomena like the spontaneous reversal of rotations. Nonholonomic models, intermediate between conservative and dissipative systems, should take their deserved place in the general picture of the modern theory of dynamical systems.

Funding Agency Grant Number
Russian Science Foundation 15-12-20035
The author is indebted to the Russian Science Foundation for the support of the work through grant No 15-12-20035.


DOI: https://doi.org/10.3367/UFNr.0185.201512h.1342

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English version:
Physics–Uspekhi, 2015, 58:12, 1223–1224

Bibliographic databases:

PACS: 05.45.-a, 45.40.-f
Received: October 8, 2015
Accepted: October 8, 2015

Citation: S. P. Kuznetsov, “On the validity of the nonholonomic model of the rattleback”, UFN, 185:12 (2015), 1342–1344; Phys. Usp., 58:12 (2015), 1223–1224

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. P. Kuznetsov, S. P. Kuznetsov, Yu. V. Sedova, “Mayatnikovaya sistema s beskonechnym chislom sostoyanii ravnovesiya i kvaziperiodicheskoi dinamikoi”, Nelineinaya dinam., 12:2 (2016), 223–234  mathnet  elib
    2. I. R. Sataev, A. O. Kazakov, “Stsenarii perekhoda k khaosu v negolonomnoi modeli volchka Chaplygina”, Nelineinaya dinam., 12:2 (2016), 235–250  mathnet  elib
    3. S. P. Kuznetsov, “Regular and Chaotic Motions of the Chaplygin Sleigh With Periodically Switched Location of Nonholonomic Constraint”, EPL, 118:1 (2017), 10007  crossref  mathscinet  isi  scopus
    4. I. A. Bizyaev, A. V. Borisov, S. P. Kuznetsov, “Chaplygin Sleigh With Periodically Oscillating Internal Mass”, EPL, 119:6 (2017), 60008  crossref  isi
    5. S. P. Kuznetsov, “Regular and Chaotic Dynamics of a Chaplygin Sleigh due to Periodic Switch of the Nonholonomic Constraint”, Regul. Chaotic Dyn., 23:2 (2018), 178–192  mathnet  crossref
  • Успехи физических наук Physics-Uspekhi
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