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Regular and Chaotic Dynamics, 2015, Volume 20, Issue 5, Pages 542–552
DOI: https://doi.org/10.1134/S1560354715050032
(Mi rcd20)
 

This article is cited in 10 scientific papers (total in 10 papers)

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

Božidar Jovanović

Mathematical Institute SANU, Kneza Mihaila 36, 11000, Belgrade, Serbia
Citations (10)
References:
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.
Received: 28.06.2015
Bibliographic databases:
Document Type: Article
MSC: 37J60, 70F25, 70H45
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
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\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
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  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:175
    References:38
     
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