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.
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