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 Nelin. Dinam., 2019, Volume 15, Number 1, Pages 87–96 (Mi nd643)

Mathematical problems of nonlinearity

On Poisson’s Theorem of Building First Integrals for Ordinary Differential Systems

A. F. Pranevich

Yanka Kupala State University of Grodno, ul. Ozechko 22, Grodno, 230023 Belarus

Abstract: We consider Hamiltonian systems with $n$ degrees of freedom. Among the general methods of integration of Hamiltonian systems, the Poisson method is of particular importance. It allows one to find the additional (third) first integral of the Hamiltonian system by two known first integrals of the Hamiltonian system. In this paper, the Poisson method of building first integrals of Hamiltonian systems by integral manifolds and partial integrals is developed. Also, the generalization of the Poisson method for general ordinary differential systems is obtained.

Keywords: Hamiltonian system, Poisson’s theorem, first integral, integral manifold, partial integral, Poisson bracket

DOI: https://doi.org/10.20537/nd190109

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MSC: 37J05, 37J15, 34C14
Accepted:19.03.2019
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Citation: A. F. Pranevich, “On Poisson’s Theorem of Building First Integrals for Ordinary Differential Systems”, Nelin. Dinam., 15:1 (2019), 87–96

Citation in format AMSBIB
\Bibitem{Pra19} \by A. F. Pranevich \paper On Poisson’s Theorem of Building First Integrals for Ordinary Differential Systems \jour Nelin. Dinam. \yr 2019 \vol 15 \issue 1 \pages 87--96 \mathnet{http://mi.mathnet.ru/nd643} \crossref{https://doi.org/10.20537/nd190109}