Geodesic
Control of the Motion of a Triaxial Ellipsoid in a Fluid Using Rotors
Matematičeskie zametki, Tome 102 (2017) no. 4, pp. 503-513.

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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. 
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A. V. Borisov; E. V. Vetchanin; A. A. Kilin. Control of the Motion of a Triaxial Ellipsoid in a Fluid Using Rotors. Matematičeskie zametki, Tome 102 (2017) no. 4, pp. 503-513. http://geodesic.mathdoc.fr/item/MZM_2017_102_4_a2/

[1] V. V. Kozlov, S. M. Ramodanov, “O dvizhenii izmenyaemogo tela v idealnoi zhidkosti”, PMM, 65:4 (2001), 592–601 | Zbl

[2] V. V. Kozlov, S. M. Ramodanov, “O dvizhenii v idealnoi zhidkosti tela s zhestkoi obolochkoi i menyayuscheisya geometriei mass”, DAN, 382:4 (2002), 478–481

[3] D. A. Onischenko, V. V. Kozlov, “O dvizhenii v idealnoi zhidkosti tela, soderzhaschego vnutri sebya podvizhnuyu sosredotochennuyu massu”, PMM, 67:4 (2003), 620–633 | MR | Zbl

[4] G. Kirchhoff, Vorlesungen über Mathematische Physik: Mechanik, B.G. Teubner, Leipzig, 1877 | Zbl

[5] A. A. Kilin, E. V. Vetchanin, “Upravlenie dvizheniem tverdogo tela v zhidkosti s pomoschyu dvukh podvizhnykh mass”, Nelineinaya dinam., 11:4 (2015), 633–645

[6] E. V. Vetchanin, A. A. Kilin, “Svobodnoe i upravlyaemoe dvizhenie v zhidkosti tela s podvizhnoi vnutrennei massoi pri nalichii tsirkulyatsii vokrug tela”, Dokl. AN, 466:3 (2016), 293–297 | MR

[7] E. V. Vetchanin, A. A. Kilin, “Control of body motion in an ideal fluid using the internal mass and the rotor in the presence of circulation around the body”, J. Dyn. Control Syst., 23:2 (2017), 435–458 | MR

[8] A. V. Borisov, A. A. Kilin, I. S. Mamaev, “How to control Chaplygin's sphere using rotors”, Regul. Chaotic Dyn., 17:3-4 (2012), 258–272 | DOI | MR | Zbl

[9] A. V. Borisov, A. A. Kilin, I. S. Mamaev, “How to control the Chaplygin ball using rotors. II”, Regul. Chaotic Dyn., 18:1-2 (2013), 144–158 | DOI | MR | Zbl

[10] T. B. Ivanova, E. N. Pivovarova, “Comments on the paper by A. V. Borisov, A. A. Kilin, I. S. Mamaev “How to control the Chaplygin ball Using rotors. II””, Regul. Chaotic Dyn., 19:1 (2014), 140–143 | DOI | MR | Zbl

[11] A. Morinaga, M. Svinin, M. Yamamoto, “On the iterative steering of a rolling robot actuated by internal rotors”, Analysis, Modelling, Optimization, and Numerical Techniques, Springer Proc. Math. Stat., 121, Springer, Cham, 2015, 205–218 | DOI | MR | Zbl

[12] P. K. Rashevskii, “O soedinimosti lyubykh dvukh tochek vpolne negolonomnogo prostranstva dopustimoi liniei”, Uchen. zap. Ped. in-ta im. Libknekhta. Ser. fiz.-matem., 3:2 (1938), 83–94

[13] A. M. Lyapunov, “O postoyannykh vintovykh dvizheniyakh tverdogo tela v zhidkosti”, Soobsch. Kharkovskogo matem. ob-va. Ser. 2, 1:1-2 (1888), 7–60

[14] P. Holmes, J. Jenkins, N. E. Leonard, “Dynamics of the Kirchhoff equations. I. Coincident centers of gravity and buoyancy”, Phys. D, 118:3-4 (1998), 311–342 | DOI | MR | Zbl

[15] J. L. G. Guirao, J. A. Vera, “Equilibria, stability and Hamiltonian Hopf bifurcation of a gyrostat in an incompressible ideal fluid”, Phys. D, 241:19 (2012), 1648–1654 | DOI | MR | Zbl

[16] C. A. Woolsey, N. E. Leonard, “Stabilizing underwater vehicle motion using internal rotors”, Automatica J. IFAC, 38:12 (2002), 2053–2062 | DOI | MR | Zbl

[17] J. Biggs, W. Holderbaum, “Optimal kinematic control of an autonomous underwater vehicle”, IEEE Trans. Automat. Control, 54:7 (2009), 1623–1626 | DOI | MR

[18] A. V. Borisov, I. S. Mamaev, Dinamika tverdogo tela. Gamiltonovy metody, integriruemost, khaos, IKI, M.–Izhevsk, 2005 | MR | Zbl