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 Tr. Mat. Inst. Steklova, 2016, Volume 295, Pages 321–351 (Mi tm3750)

Controlled motion of a rigid body with internal mechanisms in an ideal incompressible fluid

E. V. Vetchaninab, A. A. Kilinb

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

Abstract: We consider the controlled motion in an ideal incompressible fluid of a rigid body with moving internal masses and an internal rotor in the presence of circulation of the fluid velocity around the body. The controllability of motion (according to the Rashevskii–Chow theorem) is proved for various combinations of control elements. In the case of zero circulation, we construct explicit controls (gaits) that ensure rotation and rectilinear (on average) motion. In the case of nonzero circulation, we examine the problem of stabilizing the body (compensating the drift) at the end point of the trajectory. We show that the drift can be compensated for if the body is inside a circular domain whose size is defined by the geometry of the body and the value of circulation.

 Funding Agency Grant Number Russian Science Foundation 14-19-0130315-12-20035 The work of E.V. Vetchanin (Sections 2, 4 and Conclusions) is supported by the Russian Science Foundation under grant 14-19-01303 and performed at the Kalashnikov Izhevsk State Technical University. The work of A.A. Kilin (Sections 1 and 3) is supported by the Russian Science Foundation under grant 15-12-20035 and performed at the Udmurt State University.

DOI: https://doi.org/10.1134/S037196851604018X

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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 295, 302–332

Bibliographic databases:

Document Type: Article
UDC: 532.3
Received: June 14, 2016

Citation: E. V. Vetchanin, A. A. Kilin, “Controlled motion of a rigid body with internal mechanisms in an ideal incompressible fluid”, Modern problems of mechanics, Collected papers, Tr. Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 321–351; Proc. Steklov Inst. Math., 295 (2016), 302–332

Citation in format AMSBIB
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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. 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
2. E. V. Vetchanin, A. A. Kilin, “Upravlenie dvizheniem neuravnoveshennogo tyazhelogo ellipsoida v zhidkosti s pomoschyu rotorov”, Nelineinaya dinam., 12:4 (2016), 663–674
3. Yu. L. Karavaev, A. A. Kilin, A. V. Klekovkin, “Experimental investigations of the controlled motion of a screwless underwater robot”, Regul. Chaotic Dyn., 21:7-8 (2016), 918–926
4. A. I. Klenov, A. 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
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
6. 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
7. 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
8. 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
9. 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
10. 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
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