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Regul. Chaotic Dyn., 2015, Volume 20, Issue 5, Pages 542–552 (Mi rcd20)  

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

Invariant Measures of Modified $\mathrm{LR}$ and $\mathrm{L+R}$ Systems

Božidar Jovanović

Mathematical Institute SANU, Kneza Mihaila 36, 11000, Belgrade, Serbia

Abstract: We introduce a class of dynamical systems having an invariant measure, the modifications of well-known systems on Lie groups: $\mathrm{LR}$ and $\mathrm{L+R}$ systems. As an example, we study a modified Veselova nonholonomic rigid body problem, considered as a dynamical system on the product of the Lie algebra $so(n)$ with the Stiefel variety $V_{n, r}$, as well as the associated $\epsilon\mathrm{L+R}$ system on $so(n) \times V_{n, r}$. In the $3$-dimensional case, these systems model the nonholonomic problems of motion of a ball and a rubber ball over a fixed sphere.

Keywords: nonholonomic constraints, invariant measure, Chaplygin ball

Funding Agency Grant Number
Ministry of Education, Science and Technical Development of Serbia 174020
The research was supported by the Serbian Ministry of Education and Science Project 174020 Geometry and Topology of Manifolds, Classical Mechanics, and Integrable Dynamical System.


DOI: https://doi.org/10.1134/S1560354715050032

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 37J60, 70F25, 70H45
Received: 28.06.2015
Language: English

Citation: Božidar Jovanović, “Invariant Measures of Modified $\mathrm{LR}$ and $\mathrm{L+R}$ Systems”, Regul. Chaotic Dyn., 20:5 (2015), 542–552

Citation in format AMSBIB
\Bibitem{Jov15}
\by Bo{\v z}idar Jovanovi\'c
\paper Invariant Measures of Modified $\mathrm{LR}$ and $\mathrm{L+R}$ Systems
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 5
\pages 542--552
\mathnet{http://mi.mathnet.ru/rcd20}
\crossref{https://doi.org/10.1134/S1560354715050032}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3412544}
\zmath{https://zbmath.org/?q=an:06529973}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000362971400003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84944446123}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Jovanovic B., “Rolling Balls Over Spheres in R-N”, Nonlinearity, 31:9 (2018), 4006–4030  crossref  mathscinet  zmath  isi  scopus
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