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arXiv · 2210.09131

Basic notions of Poisson and symplectic geometry in local coordinates, with applications to Hamiltonian systems

Alexei A. Deriglazov
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Abstract

This work contains a brief and elementary exposition of the foundations of Poisson and symplectic geometries, with an emphasis on applications for Hamiltonian systems with second-class constraints. In particular, we clarify the geometric meaning of the Dirac bracket on a symplectic manifold and provide a proof of the Jacobi identity on a Poisson manifold. A number of applications of the Dirac bracket are described: applications for the proof of the compatibility of a system consisting of differential and algebraic equations, as well as applications for the problem of reduction of a Hamiltonian system with known integrals of motion.

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BibTeXRIS

Alexei A. Deriglazov. 2022-10-17. Basic notions of Poisson and symplectic geometry in local coordinates, with applications to Hamiltonian systems. https://doi.org/10.3390/universe8100536

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