Geodesic
Chaotic motion of top with displaced mass center
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 2, pp. 90-95.

Voir la notice de l'article provenant de la source Math-Net.Ru

The motion of solid body with a small displacement mass center from the axis of dynamic symmetry has been studied. Analytical conditions for the existence of a hyperbolic singular point in the phase portrait of the system and the analytical solution for the separatrices have been obtained. Body makes a chaotic motion near separatrices under the influence of small perturbations caused by the asymmetry of the body. Using the numerical simulation based on the Melnikov method in interpretation of Holmes–Marsden confirmation of the chaotic motion system has been received. This has been illustrated by a series of Poincare sections. 
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D. A. Losyakova. Chaotic motion of top with displaced mass center. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 2, pp. 90-95. http://geodesic.mathdoc.fr/item/ISU_2012_12_2_a12/

[1] Holmes P. J., Marsden J. E., “Horseshoes and Arnold diffusion for Hamiltonian systems on Lie groups”, Indiana University Math. J., 32:5 (1983), 273–309 | DOI | MR | Zbl

[2] Aslanov V. S., “Dvizhenie nesimmetrichnogo tvërdogo tela pod deistviem bigarmonicheskogo momenta”, Problemy analiticheskoi mekhaniki i teorii ustoichivosti, Sb. nauch. st., posvyasch. pamyati akad. V. V. Rumyantseva, Fizmatlit, M., 2009, 420 pp.

[3] Aslanov V. S., Ivanov B. V., “Khaoticheskoe dvizhenie nelineinoi sistemy”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 8:4 (2008), 38–43

[4] Aslanov V. S., Prostranstvennoe dvizhenie tela pri spuske v atmosfere, Fizmatlit, M., 2004, 160 pp.

[5] Markeev A. P., Teoreticheskaya mekhanika, uchebnik dlya universitetov, CheRo, M., 1999, 572 pp.

[6] Arnold V. I., Kozlov V. V., Neishtadt A. I., Matematicheskie aspekty klassicheskoi i nebesnoi mekhaniki, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 3, VINITI, M., 1985, 304 pp. | MR | Zbl

[7] Gukenkheimer Dzh., Kholms F., Nelineinye kolebaniya, dinamicheskie kolebaniya sistemy i bifurkatsii vektornykh polei, Institut kompyuternykh issledovanii, M.–Izhevsk, 2002, 560 pp.

[8] Melnikov V. K., “Ob ustoichivosti tsentra pri periodicheskikh po vremeni vozmuscheniyakh”, Tr. Moskovskogo mat. obschestva, 12, 1963, 1–56 | MR | Zbl

[9] Dodd R., Eilbek Dzh., Gibbon Dzh., Morris Kh., Solitony i nelineinye volnovye uravneniya, Mir, M., 1988, 694 pp. | MR

[10] Morozov A. D., Dragun T. N., Vizualizatsiya i analiz invariantnykh mnozhestv dinamicheskikh sistem, IKI, M.–Izhevsk, 2003, 304 pp.

[11] Goirgilli A., Lazutkin V. F., Simo C., “Visualization of a hyperbolic structure in area preserving maps”, Reg. Chaot. Dyn., 2:3–4 (1997), 47–61 | MR

[12] Aslanov V. S., Ledkov A. S., “Osobennosti vraschatelnogo dvizheniya kosmicheskogo apparata pri spuske v atmosfere Marsa”, Kosmicheskie issledovaniya, 45:4 (2007), 351–357