Geodesic
The dynamics of the Chaplygin ball with a fluid-filled cavity
Russian journal of nonlinear dynamics, Tome 8 (2012) no. 1, pp. 103-111.

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We consider the problem of rolling of a ball with an ellipsoidal cavity filled with an ideal fluid, which executes a uniform vortex motion, on an absolutely rough plane. We point out the case of existence of an invariant measure and show that there is a particular case of integrability under conditions of axial symmetry
Mots-clés : vortex motion
Keywords: non-holonomic constraint, Chaplygin ball, invariant measure, integrability, rigid body, ideal fluid. 
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A. V. Borisov; I. S. Mamaev. The dynamics of the Chaplygin ball with a fluid-filled cavity. Russian journal of nonlinear dynamics, Tome 8 (2012) no. 1, pp. 103-111. http://geodesic.mathdoc.fr/item/ND_2012_8_1_a6/

[1] Bolsinov A. V., Borisov A. V., Mamaev I. S., “Gamiltonizatsiya negolonomnykh sistem v okrestnosti invariantnykh mnogoobrazii”, Nelineinaya dinamika, 6:4 (2010), 829–854

[2] Borisov A. V., Kilin A. A., Mamaev I. S., “Kachenie odnorodnogo shara po dinamicheski nesimmetrichnoi sfere”, Nelineinaya dinamika, 6:4 (2010), 869–889 | MR

[3] Borisov A. V., Gazizullina L. A., Mamaev I. S., “O nasledii V. A. Steklova po klassicheskoi mekhanike”, Nelineinaya dinamika, 7:2 (2011), 389–403 | MR

[4] Borisov A. V., Kilin A. A., Mamaev I. S., “Obobschenie preobrazovaniya Chaplygina i yavnoe integrirovanie sharovogo podvesa”, Nelineinaya dinamika, 7:2 (2011), 313–338 | MR

[5] Borisov A. V., Mamaev I. S., Dinamika tverdogo tela, NITs «Regulyarnaya i khaoticheskaya dinamika», M.–Izhevsk, 2001, 384 pp.

[6] Zhukovskii N. E., “O dvizhenii tverdogo tela, imeyuschego polosti, napolnennye odnorodnoyu kapelnoi zhidkostyu: I, II, III”, Sobr. soch., v. 1, GITTL, M., 1949, 31–152

[7] Karapetyan A. V., Prokonina O. V., “Ob ustoichivosti ravnomernykh vraschenii volchka s polostyu, zapolnennoi zhidkostyu, na ploskosti s treniem”, PMM, 64:1 (2000), 85–91 | MR | Zbl

[8] Markeev A. P., “Ob ustoichivosti vrascheniya volchka s polostyu, napolnennoi zhidkostyu”, MTT, 1985, no. 3, 19–26 | MR

[9] Moiseev N. N., Rumyantsev V. V., Dinamika tverdogo tela s polostyami, soderzhaschimi zhidkost, Nauka, M., 1965, 440 pp.

[10] Rudenko T. V., “Ob ustoichivosti statsionarnykh dvizhenii girostata s zhidkostyu v polosti”, PMM, 66:2 (2002), 183–191 | MR | Zbl

[11] Steklov V. A., Raboty po mekhanike 1902–1909 gg., Perevody s frantsuzskogo, NITs «Regulyarnaya i khaoticheskaya dinamika», Izhevskii inst. kompyutern. issled., M.–Izhevsk, 2011, 492 pp.

[12] Liu Y. Z., “The stability of a fluid-filled top rotating on a horizontal plane”, Arch. Appl. Mech., 62 (1992), 487–494 | DOI | Zbl

[13] Perry J., Spinning top and gyroscopic motions, Dover, New York, 1957, 102 pp.; Perri Dzh., Vraschayuschiisya volchok, NITs «Regulyarnaya i khaoticheskaya dinamika», M.–Izhevsk, 2001, 112 pp.

[14] Poincaré H., “Sur la précession des corps déformables”, Bull. Astron., 27 (1910), 321–356 ; Пуанкаре А., Последние работы, РХД, Ижевск, 2001, 74–111 с. | MR

[15] Poincaré H., “Sur le forme nouvelle des equations de la mecanique”, C. R. Acad. Sci. Paris, 132 (1901), 369–371 ; Пуанкаре А., Последние работы, РХД, Ижевск, 2001, 72–73 с. | Zbl

[16] Rambaux N., Van Hoolst T., Dehant V., Bois E., “Inertial core-mantle coupling and libration of Mercury”, Astron. Astrophys., 468:2 (2007), 711–719 | DOI

[17] Stekloff V. A., “Sur la théorie des tourbillons”, Ann. Fac. Sci. Toulouse Math. (2), 10 (1908), 271–334 ; Steklov V. A., “O teorii vikhrei”: V. A. Steklov, Raboty po mekhanike 1902–1909 gg., Perevody s frantsuzskogo, NITs «Regulyarnaya i khaoticheskaya dinamika», Izhevskii inst. kompyutern. issled., M.–Izhevsk, 2011, 83–151 | DOI | MR | Zbl

[18] Stekloff V. A., “Sur le movement d'un corps solide ayant une cavité de forme ellipsoidale remplie par un liquide incompressible et sur les variations des latitudes”, Ann. Fac. Sci. Toulouse Math. (3), 1 (1909), 145–256 ; Steklov V. A., “O dvizhenii tverdogo tela, imeyuschego polost ellipsoidalnoi formy, zapolnennuyu neszhimaemoi zhidkostyu, i ob izmenenii shirot”, Raboty po mekhanike 1902–1909 gg., Perevody s frantsuzskogo, NITs «Regulyarnaya i khaoticheskaya dinamika», Izhevskii inst. kompyutern. issled., M.–Izhevsk, 2011, 283–408 | DOI | MR

[19] Thompson S. Ph., “Chap. 18: Gyrostatics and wave motion”, The life of William Thomson, Baron Kelvin of Largs, v. 2, McMillan, London, 1910, 736–752; Tompson S. F., “Girostatika i volnovoe dvizhenie”, (glava 18 knigi «Zhizn lorda Kelvina»), Nelineinaya dinamika, 8:1 (2012), 149–153

[20] Thomson W., “On the precessional motion of a liquid”, Nature, 15 (1877), 297–298 ; Tomson U., “O pretsessionnom dvizhenii zhidkosti”, Nelineinaya dinamika, 8:1 (2012), 9–13 | DOI

[21] Volterra V., “Sur la théorie des variations des latitedes”, Acta. Math., 22 (1899), 201–358 | DOI | MR