Issues

 / 

2015

 / 

December

  

Letters to the editors


On the validity of nonholonomic model of the rattleback


Kotel'nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Saratov Branch, ul. Zelenaya 38, Saratov, 410019, Russian Federation

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 a 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 for 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.

Text can be downloaded in Russian. English translation is available here.
Keywords: rattleback, solid body, nonholonomic model, attractor
PACS: 05.45.−a, 45.40.−f (all)
DOI: 10.3367/UFNe.0185.201512h.1342
URL: https://ufn.ru/en/articles/2015/12/g/
Citation: Kuznetsov S P "On the validity of nonholonomic model of the rattleback" Phys. Usp. 58 1223–1224 (2015)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 8th, October 2015, 8th, October 2015

Оригинал: Кузнецов С П «К вопросу о правомерности неголономной модели динамики кельтского камня» УФН 185 1342–1344 (2015); DOI: 10.3367/UFNr.0185.201512h.1342

References (21) Cited by (3) Similar articles (7) ↓

  1. A.V. Borisov, I.S. Mamaev “Notes on new friction models and nonholonomic mechanics58 1220–1222 (2015)
  2. V.F. Zhuravlev “Once more on the dynamics of the rattleback (comment on "Strange attractors in rattleback dynamics" by A.V. Borisov and I.S. Mamaev [Usp. Fiz. Nauk 173 407 (2003); Phys. Usp. 46 393 (2003)] and "Nonlinear dynamics of the rattleback: a nonholonomic model" by A.V. Borisov, A.O. Kazakov, S.P. Kuznetsov [Usp. Fiz. Nauk 184 493 (2014); Phys. Usp. 57 453 (2014)])58 1218–1219 (2015)
  3. G.R. Ivanitskii “Memory about the past is beneficial for survival and reproduction (reply to comment (Usp. Fiz. Nauk 182 1235 (2012) [Phys. Usp. 55 1152 (2012)]) by V I Klyatskin on “21st century: what is life from the perspective of physics” (Usp. Fiz. Nauk 180 337 (2010) [Phys. Usp. 53 327 (2010)]) by G R Ivanitskii)55 1155–1160 (2012)
  4. V.I. Klyatskin “Spatial structures can form in stochastic dynamic systems due to near-zero-probability events (comment on “21st century: what is life from the perspective of physics?” (Usp. Fiz. Nauk 180 337 (2010) [Phys. Usp. 53 327 (2010)]) by G R Ivanitskii)55 1152–1154 (2012)
  5. S.N. Vladimirov “Does the sign correlation of quasiperiodic oscillations with incommensurable frequencies generate deterministic chaos?47 205–208 (2004)
  6. Yu.N. Korystov “Life originated as a genetic code (contribution to the discussion of the paper by G.R. Ivanitskii "21st century: what is life from the perspective of physics" [Usp. Fiz. Nauk. 180 337 (2010); Phys. Usp. 53 327 (2010); Usp. Fiz. Nauk. 182 1235 (2012); Phys. Usp. 55 1152 (2012); Usp. Fiz. Nauk 182 1238 (2012); Phys. Usp. 55 1155 (2012)])60 219–224 (2017)
  7. E.A. Arinstein “Relation between energy conservation and dynamics (Comment on "Analytical mechanics and field theory: derivation of equations from energy conservation" by N.A. Vinokurov (Usp. Fiz. Nauk 184 641 (2014) [Phys. Usp. 57 593 (2014)]))58 309–310 (2015)

The list is formed automatically.

© 1918–2019 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions