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Regul. Chaotic Dyn., 2016, Volume 21, Issue 7-8, Pages 874–884 (Mi rcd233)  

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

Control of the Motion of a Helical Body in a Fluid Using Rotors

Evgeny V. Vetchanina, Alexander A. Kilinb, Ivan S. Mamaeva

a Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069 Russia
b Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia

Abstract: This paper is concerned with the motion of a helical body in an ideal fluid, which is controlled by rotating three internal rotors. It is proved that the motion of the body is always controllable by means of three rotors with noncoplanar axes of rotation. A condition whose satisfaction prevents controllability by means of two rotors is found. Control actions that allow the implementation of unbounded motion in an arbitrary direction are constructed. Conditions under which the motion of the body along an arbitrary smooth curve can be implemented by rotating the rotors are presented. For the optimal control problem, equations of sub-Riemannian geodesics on $SE(3)$ are obtained.

Keywords: ideal fluid, motion of a helical body, Kirchhoff equations, control of rotors, gaits, optimal control

Funding Agency Grant Number
Russian Science Foundation 14-19-01303
Russian Foundation for Basic Research 14-01-00395-a
The work of E.V.Vetchanin and I. S.Mamaev (Introduction and Sections 1 and 2) was supported by the Russian Science Foundation (project No. 14-19-01303). The work of A. A.Kilin (Section 3 and Conclusion) was supported by the Russian oundation for Basic Research No. 14-01-00395-a and No. 15-08-09093-a.


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Document Type: Article
MSC: 70Q05, 70Hxx, 76Bxx
Received: 23.11.2016
Language: English

Citation: 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

Citation in format AMSBIB
\by Evgeny V. Vetchanin, Alexander A. Kilin, Ivan S. Mamaev
\paper Control of the Motion of a Helical Body in a Fluid Using Rotors
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 7-8
\pages 874--884

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    This publication is cited in the following articles:
    1. Yury L. Karavaev, Alexander A. Kilin, Anton V. Klekovkin, “Experimental Investigations of the Controlled Motion of a Screwless Underwater Robot”, Regul. Chaotic Dyn., 21:7-8 (2016), 918–926  mathnet  crossref
    2. 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
    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. E. V. Vetchanin, V. A. Tenenev, A. A. Kilin, “Optimalnoe upravlenie dvizheniem v idealnoi zhidkosti tela s vintovoi simmetriei s vnutrennimi rotorami”, Kompyuternye issledovaniya i modelirovanie, 9:5 (2017), 741–759  mathnet  crossref
    5. E. V. Vetchanin, I. S. Mamaev, “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
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