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, Trudy Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 321–351; Proc. Steklov Inst. Math., 295 (2016), 302

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 295, Pages 321–351
DOI: https://doi.org/10.1134/S037196851604018X (Mi tm3750)

This article is cited in 16 scientific papers (total in 16 papers)

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

E. V. Vetchanin^ab, A. A. Kilin^b

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

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

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	14-19-01303 15-12-20035
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.

Received: June 14, 2016

English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 295, Pages 302–332
DOI: https://doi.org/10.1134/S0081543816080186

Bibliographic databases:

Document Type: Article

UDC: 532.3

Language: Russian

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, Trudy Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 321–351; Proc. Steklov Inst. Math., 295 (2016), 302–332

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This publication is cited in the following 16 articles:

Alexander A. Kilin, Anna M. Gavrilova, Elizaveta M. Artemova, “Dynamics of an Elliptic Foil with an Attached Vortex in an Ideal Fluid: The Integrable Case”, Regul. Chaot. Dyn., 2024
Karavaev Yu.L., Klekovkin V A., Mamaev I.S., Tenenev V.A., Vetchanin E.V., “A Simple Physical Model For Control of An Propellerless Aquatic Robot”, J. Mech. Robot., 14:1 (2022), 011007
E. M. Artemova, E. V. Vetchanin, “Control of the motion of a circular cylinder in an ideal fluid using a source”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:4 (2020), 604–617
Anton V. Klekovkin, Yury L. Karavaev, Ivan S. Mamaev, Evgeny V. Vetchanin, Valentin A. Tenenev, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 1
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
Valeriy Nikolsky, Ivan Kuzyayev, Oleksandr Alieksandrov, Viktor Ved, Andrii Pugach, Vadim Yaris, Serhiy Ptitsyn, Valerii Lopatin, “Analytical and experimental studies into the processes of hydrodynamics and heat exchange in the channels of disk pulse devices”, EEJET, 4:8 (100) (2019), 15
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
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
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
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
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
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
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
E. V. Vetchanin, A. A. Kilin, “Upravlenie dvizheniem neuravnoveshennogo tyazhelogo ellipsoida v zhidkosti s pomoschyu rotorov”, Nelineinaya dinam., 12:4 (2016), 663–674
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
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

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

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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