Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2006, Volume 2, Number 3, Pages 333–345 (Mi nd173)  
Stability of steady rotations in the non-holonomic Routh problem

A. V. Borisovab, A. A. Kilinab, I. S. Mamaevab

a Udmurt State University
b Institute of Computer Science
Full-text PDF (596 kB) (1)
Abstract: We have discovered a new first integral in the problem of motion of a dynamically symmetric ball, subject to gravity, on the surface of a paraboloid. Using this integral, we have obtained conditions for stability (in the Lyapunov sense) of steady rotations of the ball in the upmost, downmost and saddle point.
Keywords: nonholonomic constraint, stationary rotations, stability.
Document Type: Article
UDC: 531.3
MSC: 34D20, 70E40, 37J35
Language: Russian
Citation: A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Stability of steady rotations in the non-holonomic Routh problem”, Nelin. Dinam., 2:3 (2006), 333–345
Citation in format AMSBIB
\Bibitem{BorKilMam06}
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper Stability of steady rotations in the non-holonomic Routh problem
\jour Nelin. Dinam.
\yr 2006
\vol 2
\issue 3
\pages 333--345
\mathnet{http://mi.mathnet.ru/nd173}
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  • https://www.mathnet.ru/eng/nd/v2/i3/p333
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    		Нелинейная динамика
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