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Mat. Zametki, 2017, Volume 102, Issue 4, Pages 503–513 (Mi mz11399)  

This article is cited in 8 scientific papers (total in 8 papers)

Control of the Motion of a Triaxial Ellipsoid in a Fluid Using Rotors

A. V. Borisovab, E. V. Vetchaninbc, A. A. Kilinbd

a Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
b Udmurt State University, Izhevsk
c Izhevsk State Technical University
d Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: The motion of a body shaped as a triaxial ellipsoid and controlled by the rotation of three internal rotors is studied. It is proved that the motion is controllable with the exception of a few particular cases. Partial solutions whose combinations enable an unbounded motion in any arbitrary direction are constructed.

Keywords: ideal fluid, motion of a rigid body, Kirchhoff equations, control by rotors, gate.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.2404.2017/4.6
Russian Foundation for Basic Research 15-08-09093-а
15-38-20879 мол_а_вед
The work of the first author was supported by the Ministry of Education and Science of the Russian Federation under grant 1.2404.2017/4.6, The work of the second author was supported by the Russian Foundation for Basic Research under grant 15-08-09093-a. The work of the third author was supported by the Russian Foundation for Basic Research under grant 15-38-20879 mol_a_ved.


DOI: https://doi.org/10.4213/mzm11399

Full text: PDF file (540 kB)
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English version:
Mathematical Notes, 2017, 102:4, 455–464

Bibliographic databases:

Document Type: Article
UDC: 532.3
PACS: 45.80.+r
Received: 06.10.2016
Revised: 14.03.2017

Citation: A. V. Borisov, E. V. Vetchanin, A. A. Kilin, “Control of the Motion of a Triaxial Ellipsoid in a Fluid Using Rotors”, Mat. Zametki, 102:4 (2017), 503–513; Math. Notes, 102:4 (2017), 455–464

Citation in format AMSBIB
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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. Vetchanin E.V., Kilin A.A., Mamaev I.S., “Control of the Motion of a Helical Body in a Fluid Using Rotors”, Regul. Chaotic Dyn., 21:7-8 (2016), 874–884  mathnet  crossref  mathscinet  zmath  isi  scopus
    2. Karavaev Yu.L., Kilin A.A., Klekovkin A.V., “Experimental Investigations of the Controlled Motion of a Screwless Underwater Robot”, Regul. Chaotic Dyn., 21:7-8 (2016), 918–926  mathnet  crossref  mathscinet  zmath  isi  scopus
    3. 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
    4. Vetchanin E.V., Mamaev I.S., “Optimal Control of the Motion of a Helical Body in a Liquid Using Rotors”, Russ. J. Math. Phys., 24:3 (2017), 399–411  crossref  mathscinet  zmath  isi  scopus
    5. 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
    6. 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
    7. 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
    8. I. S. Mamaev, V. A. Tenenev, E. V. Vetchanin, “Dynamics of a Body with a Sharp Edge in a Viscous Fluid”, Nelineinaya dinam., 14:4 (2018), 473–494  mathnet  crossref
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