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Regul. Chaotic Dyn., 2007, Volume 12, Issue 5, Pages 531–565 (Mi rcd637)  

This article is cited in 24 scientific papers (total in 24 papers)

On the 150th anniversary of A.M.Lyapunov

Asymptotic stability and associated problems of dynamics of falling rigid body

A. V. Borisova, V. V. Kozlovb, I. S. Mamaeva

a Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

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: rigid body, ideal fluid, non-holonomic mechanics

DOI: https://doi.org/10.1134/S1560354707050061


Bibliographic databases:

MSC: 37J60
Received: 17.02.2007
Accepted:02.07.2007
Language:

Citation: A. V. Borisov, V. V. Kozlov, I. S. Mamaev, “Asymptotic stability and associated problems of dynamics of falling rigid body”, Regul. Chaotic Dyn., 12:5 (2007), 531–565

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 Regul. Chaotic Dyn.
\yr 2007
\vol 12
\issue 5
\pages 531--565
\mathnet{http://mi.mathnet.ru/rcd637}
\crossref{https://doi.org/10.1134/S1560354707050061}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2350338}
\zmath{https://zbmath.org/?q=an:1229.37107}


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

    This publication is cited in the following articles:
    1. S. V. Sokolov, S. M. Ramodanov, “Dvizhenie krugovogo tsilindricheskogo tverdogo tela, vzaimodeistvuyuschego s tochechnym vikhrem, v pole sily tyazhesti”, Nelineinaya dinam., 8:3 (2012), 617–628  mathnet
    2. E. Vetchanin, I. S. Mamaev, V. A. Tenenev, “Dvizhenie tela s peremennoi geometriei mass v vyazkoi zhidkosti”, Nelineinaya dinam., 8:4 (2012), 815–836  mathnet
    3. 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
    4. Evgeny V. Vetchanin, Ivan S. Mamaev, Valentin A. Tenenev, “The Self-propulsion of a Body with Moving Internal Masses in a Viscous Fluid”, Regul. Chaotic Dyn., 18:1-2 (2013), 100–117  mathnet  crossref  mathscinet  zmath
    5. Sergei V. Sokolov, Sergei M. Ramodanov, “Falling Motion of a Circular Cylinder Interacting Dynamically with a Point Vortex”, Regul. Chaotic Dyn., 18:1-2 (2013), 184–193  mathnet  crossref  mathscinet  zmath
    6. S. V. Sokolov, “Dvizhenie krugovogo tsilindricheskogo tverdogo tela, vzaimodeistvuyuschego s $N$ tochechnymi vikhryami, v pole sily tyazhesti”, Nelineinaya dinam., 10:1 (2014), 59–72  mathnet
    7. 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
    8. Sergey P. Kuznetsov, “Plate Falling in a Fluid: Regular and Chaotic Dynamics of Finite-dimensional Models”, Regul. Chaotic Dyn., 20:3 (2015), 345–382  mathnet  crossref  mathscinet  zmath  adsnasa
    9. S. V. Sokolov, I. S. Koltsov, “Khaoticheskoe rasseyanie tochechnogo vikhrya krugovym tsilindricheskim tverdym telom, dvizhuschimsya v pole tyazhesti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:2 (2015), 184–196  mathnet  elib
    10. E. V. Vetchanin, A. A. Kilin, “Controlled motion of a rigid body with internal mechanisms in an ideal incompressible fluid”, Proc. Steklov Inst. Math., 295 (2016), 302–332  mathnet  crossref  crossref  mathscinet  isi  elib
    11. V. A. Tenenev, E. V. Vetchanin, L. F. Ilaletdinov, “Khaoticheskaya dinamika v zadache o padenii tela vintovoi formy v zhidkosti”, Nelineinaya dinam., 12:1 (2016), 99–120  mathnet
    12. E. V. Vetchanin, A. A. Kilin, “Upravlenie dvizheniem neuravnoveshennogo tyazhelogo ellipsoida v zhidkosti s pomoschyu rotorov”, Nelineinaya dinam., 12:4 (2016), 663–674  mathnet  crossref  mathscinet  elib
    13. Alexey V. Ivanov, “Connecting Orbits of Lagrangian Systems in a Nonstationary Force Field”, Regul. Chaotic Dyn., 21:5 (2016), 510–521  mathnet  crossref
    14. Evgeny V. Vetchanin, Alexander A. Kilin, Ivan S. Mamaev, “Control of the Motion of a Helical Body in a Fluid Using Rotors”, Regul. Chaotic Dyn., 21:7-8 (2016), 874–884  mathnet  crossref
    15. E. V. Vetchanin, A. I. Klenov, “Eksperimentalnye issledovaniya padeniya vintovykh tel v zhidkosti”, Nelineinaya dinam., 13:4 (2017), 585–598  mathnet  crossref  elib
    16. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    17. I. S. Mamaev, V. A. Tenenev, E. V. Vetchanin, “Dynamics of a Body with a Sharp Edge in a Viscous Fluid”, Nelin. Dinam., 14:4 (2018), 473–494  mathnet  crossref  elib
    18. Alexey V. Borisov, Ivan S. Mamaev, Eugeny V. Vetchanin, “Dynamics of a Smooth Profile in a Medium with Friction in the Presence of Parametric Excitation”, Regul. Chaotic Dyn., 23:4 (2018), 480–502  mathnet  crossref  mathscinet
    19. Alexey V. Borisov, Ivan S. Mamaev, Evgeny V. Vetchanin, “Self-propulsion of a Smooth Body in a Viscous Fluid Under Periodic Oscillations of a Rotor and Circulation”, Regul. Chaotic Dyn., 23:7-8 (2018), 850–874  mathnet  crossref
    20. Ivan S. Mamaev, Evgeny V. Vetchanin, “The Self-propulsion of a Foil with a Sharp Edge in a Viscous Fluid Under the Action of a Periodically Oscillating Rotor”, Regul. Chaotic Dyn., 23:7-8 (2018), 875–886  mathnet  crossref  mathscinet
    21. A. A. Kilin, A. I. Klenov, V. A. Tenenev, “Upravlenie dvizheniem tela s pomoschyu vnutrennikh mass v vyazkoi zhidkosti”, Kompyuternye issledovaniya i modelirovanie, 10:4 (2018), 445–460  mathnet  crossref
    22. E. V. Vetchanin, “The Motion of a Balanced Circular Cylinder in an Ideal Fluid Under the Action of External Periodic Force and Torque”, Rus. J. Nonlin. Dyn., 15:1 (2019), 41–57  mathnet  crossref  elib
    23. Alexey V. Ivanov, “On Transversal Connecting Orbits of Lagrangian Systems in a Nonstationary Force Field: the Newton Kantorovich Approach”, Regul. Chaotic Dyn., 24:4 (2019), 392–417  mathnet  crossref  mathscinet
    24. Borisov V A., Vetchanin E.V., Mamaev I.S., “Motion of a Smooth Foil in a Fluid Under the Action of External Periodic Forces. i”, Russ. J. Math. Phys., 26:4 (2019), 412–427  crossref  mathscinet  zmath  isi  scopus
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