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

    Received 21 August 2018

    2019, Vol. 15, no. 1, pp.  87-96

    Author(s): Pranevich A. F.

    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
    Citation: Pranevich A. F., On Poisson’s Theorem of Building First Integrals for Ordinary Differential Systems, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 1, pp.  87-96

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