Basic notions of poisson and symplectic geometry in local coordinates, with applications to Hamiltonian systems A. A. Deriglazov
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ArticleContent type: Текст Media type: электронный Subject(s): пуассонова геометрия | симплектическая геометрия | гамильтоновы системыGenre/Form: статьи в журналах Online resources: Click here to access online
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Universe Vol. 8, № 10. P. 536 (1-43)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 proof of the compatibility of a system consisting of differential and algebraic equations, as well as applications for the problem of the reduction of a Hamiltonian system with known integrals of motion.
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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 proof of the compatibility of a system consisting of differential and algebraic equations, as well as applications for the problem of the reduction of a Hamiltonian system with known integrals of motion.
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