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Nelin. Dinam., 2016, Volume 12, Number 4, Pages 651–661 (Mi nd544)  

Original papers

On asymptotic motions of a heavy rigid body in the Bobylev–Steklov case

G. V. Gorr

Department of applied mechanics, State Institution “Institute of Applied Mathematics and Mechanics”, ul. Rose Luxembourg 74, Donetsk, 83114, DPR

Abstract: The Bobylev–Steklov solution belongs to one of the most well-known particular solutions of the Euler–Poisson equation of the problem of motion of a heavy rigid body with a fixed point. It is characterized by two linear invariant relations and can be expressed as elliptic functions of time. The interpretation of the motion of the Bobylev–Steklov gyroscope was carried out by P.V. Kharlamov using the Poinsot method. Analysis of the neighborhood of the Bobylev–Steklov solution in the integral manifold of the Euler–Poisson equations was presented by B.S. Bardin for the case where this solution describes pendulum motions. It is therefore of interest to study the general case of the above-mentioned manifold. Using the first Lyapunov method, a new class of asymptotic motions is obtained for a heavy rigid body whose limit motions are described by the Bobylev–Steklov solution.

Keywords: the first Lyapunov method, Bobylev–Steklov solution

DOI: https://doi.org/10.20537/nd1604008

Full text: PDF file (269 kB)
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Document Type: Article
UDC: 531.38
MSC: 70E05, 70E17
Received: 05.05.2016
Accepted:09.08.2016

Citation: G. V. Gorr, “On asymptotic motions of a heavy rigid body in the Bobylev–Steklov case”, Nelin. Dinam., 12:4 (2016), 651–661

Citation in format AMSBIB
\Bibitem{Gor16}
\by G.~V.~Gorr
\paper On asymptotic motions of a heavy rigid body in the Bobylev–Steklov case
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 4
\pages 651--661
\mathnet{http://mi.mathnet.ru/nd544}
\crossref{https://doi.org/10.20537/nd1604008}
\elib{http://elibrary.ru/item.asp?id=27715769}


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