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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.
Received: 21.08.2018 Accepted: 19.03.2019
Citation:
A. F. Pranevich, “On Poisson’s Theorem of Building First Integrals for Ordinary Differential Systems”, Rus. J. Nonlin. Dyn., 15:1 (2019), 87–96
Linking options:
https://www.mathnet.ru/eng/nd643 https://www.mathnet.ru/eng/nd/v15/i1/p87
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Abstract page: | 200 | Full-text PDF : | 74 | References: | 35 |
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