Russian Journal of Nonlinear Dynamics
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Russian Journal of Nonlinear Dynamics, 2020, Volume 16, Number 3, Pages 517–525
DOI: https://doi.org/10.20537/nd200308 (Mi nd725) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Methodological notes

Estimates of Solutions During Motion of the Euler –Poinsot Top and Explanation of the Experiment with Dzhanibekov’s Nut

V. F. Zhuravleva, G. M. Rozenblatb

a Institute for Problems in Mechanics of the Russian Academy of Sciences, prosp. Vernadskogo 101, Moscow, 119526 Russia
b Moscow Automobile and Road Construction State Technical University, Leningradsky prosp. 64, Moscow, 125319 Russia
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DOI: https://doi.org/10.20537/nd200308
Abstract: This paper presents secure upper and lower estimates for solutions to the equations of rigid body motion in the Euler case (in the absence of external torques). These estimates are expressed by simple formulae in terms of elementary functions and are used for solutions that are obtained in a neighborhood of the unstable steady rotation of the body about its middle axis of inertia. The estimates obtained are applied for a rigorous explanation of the flip-over phenomenon which arises in the experiment with Dzhanibekov’s nut.
Keywords: Euler top, permanent (steady) rotation, middle axis of inertia, estimates of solutions to differential equations.
Received: 26.11.2019
Accepted: 24.08.2020
Bibliographic databases:
Document Type: Article
MSC: 70E15
Language: English
Citation: V. F. Zhuravlev, G. M. Rozenblat, “Estimates of Solutions During Motion of the Euler –Poinsot Top and Explanation of the Experiment with Dzhanibekov’s Nut”, Rus. J. Nonlin. Dyn., 16:3 (2020), 517–525
Citation in format AMSBIB
\Bibitem{ZhuRoz20}
\by V. F. Zhuravlev, G. M. Rozenblat
\paper Estimates of Solutions During Motion
of the Euler –Poinsot Top and Explanation
of the Experiment with Dzhanibekov’s Nut
\jour Rus. J. Nonlin. Dyn.
\yr 2020
\vol 16
\issue 3
\pages 517--525
\mathnet{http://mi.mathnet.ru/nd725}
\crossref{https://doi.org/10.20537/nd200308}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4159471}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85095454181}
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  • https://www.mathnet.ru/eng/nd/v16/i3/p517
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Russian Journal of Nonlinear Dynamics
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