Bifurcations in dynamics of the Chaplygin ball
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2021), pp. 64-68
Sh. M. Magomedov. Bifurcations in dynamics of the Chaplygin ball. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2021), pp. 64-68. http://geodesic.mathdoc.fr/item/VMUMM_2021_5_a9/
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     author = {Sh. M. Magomedov},
     title = {Bifurcations in dynamics of the {Chaplygin} ball},
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     pages = {64--68},
     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2021_5_a9/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The stationary motions of an inhomogeneous dynamically symmetric ball on an absolutely rough plane are studied in the special case of the center of mass passing the highest point. The system is analyzed numerically, and the existence of stable and unstable precessions is found. The results are presented in the form of bifurcation diagrams.

[1] Karapetyan A. V., “O spetsifike primeneniya teorii Rausa k sistemam s differentsialnymi svyazyami”, Prikl. matem. i mekhan., 58:3 (1994), 17–22 | Zbl

[2] Karapetyan A. V., Kuleshov A. S., “Metody issledovaniya ustoichivosti i bifurkatsii statsionarnykh dvizhenii konservativnykh negolonomnykh sistem”, Problemy mekhaniki, Sb. statei. K 90-letiyu so dnya rozhdeniya A. Yu. Ishlinskogo, ed. D.M. Klimov, Fizmatlit, M., 2003

[3] Rubanovskii V. N., Samsonov V. A., Ustoichivost statsionarnykh dvizhenii v primerakh i zadachakh, Nauka, M., 1988

[4] Karapetyan A. V., Ustoichivost statsionarnykh dvizhenii, URSS, M., 1998