论文标题
当地坐标中泊松和符号几何形状的基本概念，并应用于哈密顿系统
Basic notions of Poisson and symplectic geometry in local coordinates, with applications to Hamiltonian systems
论文作者
论文摘要
这项工作包含了泊松基础和符号几何形状基础的简短而基本的解释，重点是对具有二等限制的哈密顿系统的应用。特别是，我们在象征性的歧管上阐明了狄拉克支架的几何含义，并在泊松歧管上提供了雅各比身份的证明。描述了狄拉克支架的许多应用：用于证明由差分和代数方程组成的系统的兼容性证明，以及减少具有已知运动积分的汉密尔顿系统的问题的应用。
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.
