Based on the fact that the interval deformation energy depends only on the two end displacements vector, we derive the Lagrange and Poisson brackets analytically, the symplectic duality system, the canonical equations, and the canonical transformations, etc. 根据区段单元变形能只与其两端位移有关,就可通过数学分析得到Lagrange括号与Poisson括号,展示了其辛对偶体系、正则方程、正则变换等的内容。
Dirac connected the quantum mechanical commutators with the classical Poisson brackets, and established the transformation theory for non-relativistic quantum mechanics. Dirac把量子力学的对易关系类比于经典力学中的泊松括号(PB),建立起非相对论量子力学中的普遍变换理论.但是该理论本身能否再发展呢?
With it the canonical equations in equilibrium thermodynamics, i.e. the basic Poisson's brackets can be proved. 证明了平衡态热力学中的基本Poisson括号成立。
We express the first integrals for the system of Hamilton's canonical equations make use of Poisson's brackets, especially, prove Jacobi's identity briefly. 由Poisson括弧表达正则方程组的首次积分,特别是,较简洁地证明了Jacobi恒等式。
The third order solution of vinti's problem and the poisson's brackets of elements Vinti问题三阶解及其基本根数系统的泊松括号(PB)