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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, Issue 4, Pages 146–155 (Mi vuu356)  

This article is cited in 4 scientific papers (total in 4 papers)

MECHANICS

Stability analysis of periodic solutions in the problem of the rolling of a ball with a pendulum

E. N. Pivovarova, T. B. Ivanova

Department of Theoretical Physics, Udmurt State University, Izhevsk, Russia

Abstract: In the paper we study the stability of a spherical shell rolling on a horizontal plane with Lagrange's gyroscope inside. A linear stability analysis is made for the upper and lower position of a top. A bifurcation diagram of the system is constructed. The trajectories of the contact point for different values of the integrals of motion are constructed and analyzed.

Keywords: rolling motion, stability, Lagranges gyroscope, bifurcational diagram.

Full text: PDF file (709 kB)
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Document Type: Article
UDC: 531.31
MSC: 37J60
Received: 13.08.2012

Citation: E. N. Pivovarova, T. B. Ivanova, “Stability analysis of periodic solutions in the problem of the rolling of a ball with a pendulum”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, no. 4, 146–155

Citation in format AMSBIB
\Bibitem{PivIva12}
\by E.~N.~Pivovarova, T.~B.~Ivanova
\paper Stability analysis of periodic solutions in the problem of the rolling of a~ball with a~pendulum
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2012
\issue 4
\pages 146--155
\mathnet{http://mi.mathnet.ru/vuu356}


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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. T. B. Ivanova, E. N. Pivovarova, “Dinamika i upravlenie sfericheskim robotom s osesimmetrichnym mayatnikovym privodom”, Nelineinaya dinam., 9:3 (2013), 507–520  mathnet  crossref
    2. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dinamika negolonomnykh sistem, sostoyaschikh iz sfericheskoi obolochki s podvizhnym tverdym telom vnutri”, Nelineinaya dinam., 9:3 (2013), 547–566  mathnet
    3. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Nonholonomic Systems Consisting of a Spherical Shell with a Moving Rigid Body Inside”, Regul. Chaotic Dyn., 19:2 (2014), 198–213  mathnet  crossref  mathscinet  zmath
    4. Alexander A. Kilin, Elena N. Pivovarova, “The Rolling Motion of a Truncated Ball Without Slipping and Spinning on a Plane”, Regul. Chaotic Dyn., 22:3 (2017), 298–317  mathnet  crossref  mathscinet
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