Regular and Chaotic Dynamics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Regular and Chaotic Dynamics, 2019, Volume 24, Issue 5, Pages 511–524
DOI: https://doi.org/10.1134/S1560354719050058
(Mi rcd1024)
 

This article is cited in 1 scientific paper (total in 1 paper)

Sergey Chaplygin Memorial Issue

Nonholonomic Noetherian Symmetries and Integrals of the Routh Sphere and the Chaplygin Ball

Miguel D. Bustamante, Peter Lynch

School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland
Citations (1)
References:
Abstract: The dynamics of a spherical body with a non-uniform mass distribution rolling on a plane were discussed by Sergey Chaplygin, whose 150th birthday we celebrate this year. The Chaplygin top is a non-integrable system, with a colourful range of interesting motions. A special case of this system was studied by Edward Routh, who showed that it is integrable. The Routh sphere has a centre of mass offset from the geometric centre, but it has an axis of symmetry through both these points, and equal moments of inertia about all axes orthogonal to the symmetry axis. There are three constants of motion: the total energy and two quantities involving the angular momenta.
It is straightforward to demonstrate that these quantities, known as the Jellett and Routh constants, are integrals of the motion. However, their physical significance has not been fully understood. In this paper, we show how the integrals of the Routh sphere arise from Emmy Noether’s invariance identity. We derive expressions for the infinitesimal symmetry transformations associated with these constants. We find the finite version of these symmetries and provide their geometrical interpretation.
As a further demonstration of the power and utility of this method, we find the Noetherian symmetries and corresponding integrals for a system introduced recently, the Chaplygin ball on a rotating turntable, confirming that the known integrals are directly obtained from Noether’s theorem.
Keywords: Noether’s theorem, nonholonomic systems, symmetry, Routh sphere, Chaplygin ball.
Received: 31.05.2019
Accepted: 27.08.2019
Bibliographic databases:
Document Type: Article
Language: English
Citation: Miguel D. Bustamante, Peter Lynch, “Nonholonomic Noetherian Symmetries and Integrals of the Routh Sphere and the Chaplygin Ball”, Regul. Chaotic Dyn., 24:5 (2019), 511–524
Citation in format AMSBIB
\Bibitem{BusLyn19}
\by Miguel D. Bustamante, Peter Lynch
\paper Nonholonomic Noetherian Symmetries and Integrals of the Routh Sphere and the Chaplygin Ball
\jour Regul. Chaotic Dyn.
\yr 2019
\vol 24
\issue 5
\pages 511--524
\mathnet{http://mi.mathnet.ru/rcd1024}
\crossref{https://doi.org/10.1134/S1560354719050058}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4015394}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000488949000004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85073259519}
Linking options:
  • https://www.mathnet.ru/eng/rcd1024
  • https://www.mathnet.ru/eng/rcd/v24/i5/p511
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:136
    References:30
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024