Geodesic
Steady and periodic modes in the problem of motion of a heavy material point on a rotating sphere (the viscous friction case)
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2014), pp. 43-50 
E. S. Shalimova. Steady and periodic modes in the problem of motion of a heavy material point on a rotating sphere (the viscous friction case). Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2014), pp. 43-50. http://geodesic.mathdoc.fr/item/VMUMM_2014_4_a6/
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     author = {E. S. Shalimova},
     title = {Steady and periodic modes in the problem of motion of a heavy material point on a rotating sphere (the viscous friction case)},
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     pages = {43--50},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of motion of a heavy material point on a sphere uniformly rotating about a fixed axis is considered in the case of viscous friction. The angle of inclination between the axis and the horizon is constant. The existence, bifurcation, and stability of the equilibrium positions are discussed. The existence of periodic motions is also studied. An approach is proposed to find such motions in the case of low viscosity.

[1] Aret V.A., Orlov V.V., Zelenkov S.K., “Vybor peremeshivayuschego ustroistva na osnove postroeniya ego morfologicheskoi modeli”, Protsessy i apparaty pischevykh proizvodstv, 2009, no. 2, 1–5

[2] Akpolat Z.H., Asher G.M., Clare J.C., “Dynamic emulation of mechanical loads using a vector-controlled induction motor-generator set”, IEEE Trans. Ind. Electron., 46:2 (1999), 370–379 | DOI

[3] Papadopoulos E., Papadimitriou I., “Modeling, design and control of a portable washing machine during the spinning cycle”, Proc. 2001 IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics Systems, AIM 2001 (8–11 July 2001, Como, Italy), 2001, 899–904 | DOI

[4] Joshi P., Nigam K.D.P., Nauman E.B., “The Kenics static mixer: new data and proposed correlations”, Chem. Eng. J., 59:3 (1995), 265–271

[5] Wouw N. van de, Heuvel M.N. van Den, Nijmeijer H., Rooij J.A. van, “Performance of an automatic ball balancer with dry friction”, Int. J. Bifurc. Chaos, 15:1 (2005), 65–82 | DOI | Zbl

[6] Fleissner F., Lehnart A., Eberhard P., “Dynamic simulation of sloshing fluid and granular cargo in transport vehicles”, Vehicle System Dynamics, 48:1 (2010), 3–15 | DOI

[7] Alkhaldi H., Ergenzinger C., Fleissner F., Eberhard P., “Comparison between two different mesh descriptions used for simulation of sieving processes”, Granular Matter., 10:3 (2008), 223–229 | DOI | Zbl

[8] Pontryagin L.S., “O dinamicheskikh sistemakh, blizkikh k gamiltonovym”, Zhurn. ekperim. i teor. fiz., 4:9 (1934), 234–238

[9] Kozlov V.V., Metody kachestvennogo analiza v dinamike tverdogo tela, Izd-vo MGU, M., 1980 | MR

[10] Kozlov V.V., “Rasscheplenie separatris i rozhdenie izolirovannykh periodicheskikh reshenii v gamiltonovykh sistemakh s polutora stepenyami svobody”, Uspekhi matem. nauk, 41:5 (1986), 177–178 | MR