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Nelin. Dinam., 2007, Volume 3, Number 3, Pages 255–296 (Mi nd140)  

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

Asymptotic stability and associated problems of dynamics of falling rigid body

A. V. Borisovabc, V. V. Kozlovd, I. S. Mamaevabc

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

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.

Full text: PDF file (1653 kB)

Document Type: Article
MSC: 74F10, 93D20

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}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Borisov, L. A. Gazizullina, I. S. Mamaev, “O nasledii V. A. Steklova po klassicheskoi mekhanike”, Nelineinaya dinam., 7:2 (2011), 389–403  mathnet
    2. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. 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  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. 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  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
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