Аннотация:
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.
Ключевые слова:
ideal fluid, motion of a helical body, Kirchhoff equations, control of rotors, gaits, optimal control.
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.
Поступила в редакцию: 23.11.2016 Принята в печать: 06.12.2016
Образец цитирования:
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
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd233
https://www.mathnet.ru/rus/rcd/v21/i7/p874
Эта публикация цитируется в следующих 7 статьяx:
A. V. Borisov, E. V. Vetchanin, I. S. Mamaev, “Motion of a smooth foil in a fluid under the action of external periodic forces. II”, Russ. J. Math. Phys., 27:1 (2020), 1–17
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
А. В. Борисов, И. С. Мамаев, И. А. Бизяев, “Динамические системы с неинтегрируемыми связями: вакономная механика, субриманова геометрия и неголономная механика”, УМН, 72:5(437) (2017), 3–62; 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
Е. В. Ветчанин, В. А. Тененев, А. А. Килин, “Оптимальное управление движением в идеальной жидкости тела с винтовой симметрией с внутренними роторами”, Компьютерные исследования и моделирование, 9:5 (2017), 741–759
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
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
Е. В. Ветчанин, А. А. Килин, “Управление движением неуравновешенного тяжелого эллипсоида в жидкости с помощью роторов”, Нелинейная динам., 12:4 (2016), 663–674
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