A. V. Borisov, V. V. Kozlov, I. S. Mamaev, “Asymptotic stability and associated problems of dynamics of falling rigid body”, Nelin. Dinam., 3:3 (2007), 255

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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]

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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2007, Volume 3, Number 3, Pages 255–296 (Mi nd140)

This article is cited in 5 scientific papers (total in 5 papers)

Asymptotic stability and associated problems of dynamics of falling rigid body

A. V. Borisov^abc, V. V. Kozlov^d, I. S. Mamaev^abc

^a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
^b Udmurt State University
^c Institute of Computer Science
^d Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (1653 kB) Citations (5)

Abstract: We consider two problems from the rigid body dynamics and use new methods of stability and asymptotic behavior analysis for their solution. The first problem deals with motion of a rigid body in an unbounded volume of ideal fluid with zero vorticity. The second problem, having similar asymptotic behavior, is concerned with motion of a sleigh on an inclined plane. The equations of motion for the second problem are non-holonomic and exhibit some new features not typical for Hamiltonian systems. A comprehensive survey of references is given and new problems connected with falling motion of heavy bodies in fluid are proposed.

Keywords: nonholonomic mechanics, rigid body, ideal fluid, resisting medium.

Document Type: Article

MSC: 74F10, 93D20

Language: Russian

Citation: A. V. Borisov, V. V. Kozlov, I. S. Mamaev, “Asymptotic stability and associated problems of dynamics of falling rigid body”, Nelin. Dinam., 3:3 (2007), 255–296

Citation in format AMSBIB

\Bibitem{BorKozMam07}

\by A.~V.~Borisov, V.~V.~Kozlov, I.~S.~Mamaev

\paper Asymptotic stability and associated problems of dynamics of falling rigid body

\jour Nelin. Dinam.

\yr 2007

\vol 3

\issue 3

\pages 255--296

\mathnet{http://mi.mathnet.ru/nd140}

Linking options:

https://www.mathnet.ru/eng/nd140

https://www.mathnet.ru/eng/nd/v3/i3/p255

This publication is cited in the following 5 articles:

A. A. Tikhonov, “Dinamika tverdogo tela ot uravnenii Eilera do upravleniya uglovym dvizheniem ISZ v trudakh uchenykh SPbGU. Ch. 1”, Vestnik Sankt-Peterburgskogo universiteta. Matematika. Mekhanika. Astronomiya, 10:3 (2023), 457–486
G. E. Grishanina, N. G. Inozemtseva, M. B. Sadovnikova, “On the Deformation Method of Study of Global Asymptotic Stability”, Math. Notes, 95:3 (2014), 316–323
G. E. Grishanina, N. G. Inozemtseva, M. B. Sadovnikova, “A study of the global asymptotic stability of a one-parameter family of systems”, Dokl. Math., 89:1 (2014), 110–111
G. E. Grishanina, N. G. Inozemtseva, B. I. Sadovnikov, “On Global Asymptotic Stability and Stability of Saddle Solutions at Infinity”, Math. Notes, 93:4 (2013), 624–628
A. V. Borisov, L. A. Gazizullina, I. S. Mamaev, “O nasledii V. A. Steklova po klassicheskoi mekhanike”, Nelineinaya dinam., 7:2 (2011), 389–403

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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