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Dynamics of the Tippe Top on a Vibrating Base

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dc.contributor.authorBorisov, A. V.
dc.contributor.authorIvanov, A. P.
dc.contributor.authorИванов, Александр Павлович
dc.date.accessioned2024-11-27T10:30:51Z
dc.date.available2024-11-27T10:30:51Z
dc.date.issued2020
dc.description.abstract© 2020, Pleiades Publishing, Ltd.This paper studies the conditions under which the tippe top invertsin the presence of vibrations of the base along the vertical. A vibrational potential is constructed by averaging andit is shown that, when this potential is added to the system, the Jellett integral is preserved. Thismakes it possible to apply the modified Routh method and to find the effective potential to whose critical pointspermanent rotations or regular precessions of the tippe top correspond. Tippe top inversion is possible fora sufficiently large initial angular velocity under the condition that spinning with the lowest position of the center of gravityis unstable, spinning with the highest position of the center of gravity is stable, and that there are no precessions.Cases are found in which there is no inversion in the absence of vibrations, but it can be brought about by a suitable choice ofthe mean value of the squared velocity of the base. In particular, this type includes a ball with a spherical cavity filled witha denser substance.
dc.format.extentС. 707-715
dc.identifier.citationBorisov, A. V. Dynamics of the Tippe Top on a Vibrating Base / Borisov, A.V., Ivanov, A.P. // Regular and Chaotic Dynamics. - 2020. - 25. - № 6. - P. 707-715. - 10.1134/S1560354720060131
dc.identifier.doi10.1134/S1560354720060131
dc.identifier.urihttps://www.doi.org/10.1134/S1560354720060131
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dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/22662
dc.relation.ispartofRegular and Chaotic Dynamics
dc.titleDynamics of the Tippe Top on a Vibrating Base
dc.typeArticle
dspace.entity.typePublication
oaire.citation.issue6
oaire.citation.volume25
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