title: The attraction basin in the generalized Kapitsa’s problem
metadata.name: dc.contributor.author
metadata.value: Kulizhnikov, Dmitriy B.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Tovstik, Petr E.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Tovstik, Tatiana P.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-09-05T18:22:47Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-09-05T18:22:47Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Kulizhnikov D.B., Tovstik P.E., Tovstik T. P. The attraction basin in the generalized Kapitsa’s problem. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 3, pp. 482–492.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.312
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16324
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The attraction basin of a stable vertical position of rod under vertical vibration of the support in the Kapitsa’s problem and its generalizations is studied. A long enough flexible rod with a free upper end and a clumped lower end under its weight is shown to be unstable. The support is assumed to be subjected to harmonic vibrations. In the resent works it is established that under some level of vibrations the vertical position becomes stable. Here the attraction basin of this position is discussed. As a first step the attraction basin in the classic Kapitsa’s problem is found. Then a rigid rod with the elastic support of a lower end is studied. The last problem is a model of a flexible rod with the clumped end. The asymptotic method of two-scaled expansions is used. It is established that a transition in the vertical position essentially depends on the initial phase of vibrations. As a result it occurs that the attraction basin consists of two parts. In one of them this transition does not depend on the initial phase, and in the other part a dependence on the initial phase has place.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported by Russian Foundation for Basic Research (grants NN19.01.00280-а, 16.51.52025 МНТ-а).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 6 (64); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: generalized Kapitsa’s problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: attraction basin of a vertical position
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: two-scaled expansions
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: The attraction basin in the generalized Kapitsa’s problem
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 482-492.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16324/1/482-492.pdf
resources.format: Adobe PDF
resources.size: 439,34 kB