title: The Jacobi - Poisson Method of Building First Integrals for System of Ordinary Differential Equations
metadata.name: dc.contributor.author
metadata.value: Pranevich, Andrei
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-01-10T12:12:54Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-01-10T12:12:54Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-12
metadata.lang: -
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu35.2023.406
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/44575
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this paper, the Jacobi-Poisson method of building first integrals by known integral manifolds for Hamiltonian differential systems is developed. The existence theorem of first integrals in the form of Poisson brackets from known integral manifolds for Hamiltonian systems is proved. The statement of finding additional first integrals by known first integrals and integral manifolds for Hamiltonian systems is given. In the case of polynomial Hamiltonian systems, we use the concept of partial integrals and concretize ours results. The Jacobi - Poisson method of construction first integrals in the form of Poisson brackets from known integral characteristics (integral manifolds, partial integrals, and first integrals) for general ordinary differential systems is proposed. Statements of finding first integrals for an ordinary differential system by integral characteristics of the auxiliary Hamiltonian system are obtained. The generalized Poisson theorem of construction first integrals is indicated. And, the question of the existence of partial integrals and first integrals in the form of Poisson brackets for ordinary polynomial differential systems is investigated. The results obtained in this paper can be used in the analytical theory of differential equations and in the analytical mechanics.
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: Differential Equations and Control Processes;Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: ordinary differential system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Hamiltonian system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Jacobi – Poisson theorem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: first integral
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: integral manifold
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: partial integral
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Poisson bracket
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: The Jacobi - Poisson Method of Building First Integrals for System of Ordinary Differential Equations
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 125-141.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/44575/1/125-141.pdf
resources.format: Adobe PDF
resources.size: 699,67 kB