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Nelin. Dinam., 2015, Volume 11, Number 4, Pages 633–645 (Mi nd498)  

This article is cited in 9 scientific papers (total in 9 papers)

Original papers

The control of the motion through an ideal fluid of a rigid body by means of two moving masses

A. A. Kilinab, E. V. Vetchaninc

a Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia
b Institute of Mathematics and Mechanics of the Ural Branch of RAS ul. S. Kovalevskoi 16, Ekaterinburg, 620990, Russia
c M.T.Kalashnikov Izhevsk State Technical University, Studencheskaya st. 7, Izhevsk, 426069, Russia

Abstract: In this paper we consider the problem of motion of a rigid body in an ideal fluid with two material points moving along circular trajectories. The controllability of this system on the zero level set of first integrals is shown. Elementary “gaits” are presented which allow the realization of the body’s motion from one point to another. The existence of obstacles to a controlled motion of the body along an arbitrary trajectory is pointed out.

Keywords: ideal fluid, Kirchhoff equations, controllability of gaits

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00395-a
15-08-09093-a


Full text: PDF file (413 kB)
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Document Type: Article
UDC: 532.3
MSC: 70Q05, 70Hxx, 76Bxx
Received: 03.09.2015
Revised: 20.11.2015

Citation: A. A. Kilin, E. V. Vetchanin, “The control of the motion through an ideal fluid of a rigid body by means of two moving masses”, Nelin. Dinam., 11:4 (2015), 633–645

Citation in format AMSBIB
\Bibitem{KilVet15}
\by A.~A.~Kilin, E.~V.~Vetchanin
\paper The control of the motion through an ideal fluid of a rigid body by means of two moving masses
\jour Nelin. Dinam.
\yr 2015
\vol 11
\issue 4
\pages 633--645
\mathnet{http://mi.mathnet.ru/nd498}


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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. I. Klenov, E. V. Vetchanin, A. A. Kilin, “Eksperimentalnoe opredelenie prisoedinennykh mass tela metodom buksirovki”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:4 (2015), 568–582  mathnet  elib
    2. 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
    3. 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
    4. Anatolii I. Klenov, Alexander A. Kilin, “Influence of Vortex Structures on the Controlled Motion of an Above-water Screwless Robot”, Regul. Chaotic Dyn., 21:7-8 (2016), 927–938  mathnet  crossref
    5. 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
    6. A. V. Borisov, E. V. Vetchanin, A. A. Kilin, “Control of the Motion of a Triaxial Ellipsoid in a Fluid Using Rotors”, Math. Notes, 102:4 (2017), 455–464  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration”, Regul. Chaotic Dyn., 22:8 (2017), 955–975  mathnet  crossref
    8. E. A. Mityushov, N. E. Misyura, S. A. Berestova, “Optimalnaya stabilizatsiya kosmicheskogo apparata v inertsialnoi sisteme koordinat na baze besplatformennoi inertsialnoi navigatsionnoi sistemy”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:2 (2018), 252–259  mathnet  crossref  elib
    9. 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
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