Abstract:
We consider a mechanical system inside a rolling ball and show that if the constraints have spherical symmetry, the equations of motion have Lagrangian form. Without symmetry, this is not true.
Keywords:
nonholonomic constraint, rolling ball, Lagrange equations, Hamilton principle.
This research was done at the Udmurt State University and was supported by the Grant Program of the Government of the Russian Federation for state support of scientific research conducted under the supervision of leading scientists at Russian institutions of higher professional education (Contract №11.G34.31.0039). Also supported by the Programme “Dynamical Systems and Control Theory”.
\Bibitem{BolPop13}
\by S. V. Bolotin, T. V. Popova
\paper On the Motion of a Mechanical System Inside a Rolling Ball
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 1-2
\pages 159--165
\mathnet{http://mi.mathnet.ru/rcd102}
\crossref{https://doi.org/10.1134/S1560354713010115}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3040989}
\zmath{https://zbmath.org/?q=an:1303.37020}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000317623400011}
Linking options:
https://www.mathnet.ru/eng/rcd102
https://www.mathnet.ru/eng/rcd/v18/i1/p159
This publication is cited in the following 12 articles:
Citation in format AMSBIB
Contact us: