论文标题
操作古典力学：自动系统
Operational classical mechanics: Holonomic Systems
论文作者
论文摘要
我们构建了经典力学的操作公式，而没有以分析力学的先前结果为前提。这样，将从一个全新的角度重新发现分析机制的几个概念。首先，我们表达了点粒子位置和速度的基本概念，作为在合适的希尔伯特空间上作用的自聚算子的特征值。人类约束的概念被证明等于限制自由希尔伯特空间的线性子空间。 The principal results we obtain are: (1) the Lagrange equations of motion are derived without the use of D'Alembert or Hamilton principles, (2) the constraining forces are obtained without the use of Lagrange multipliers, (3) the passage from a position-velocity to a position-momentum description of the movement is done without the use of a Legendre transformation, (4) the Koopman-von Neumann theory is obtained as a result of our从头开始操作方法，（5）先前关于经典系统的Schwinger Action原则的工作已概括为包括自动限制。
We construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts from analytical mechanics will be rediscovered from an entirely new perspective. We start by expressing the basic concepts of the position and velocity of point particles as the eigenvalues of self-adjoint operators acting on a suitable Hilbert space. The concept of Holonomic constraint is shown to be equivalent to a restriction to a linear subspace of the free Hilbert space. The principal results we obtain are: (1) the Lagrange equations of motion are derived without the use of D'Alembert or Hamilton principles, (2) the constraining forces are obtained without the use of Lagrange multipliers, (3) the passage from a position-velocity to a position-momentum description of the movement is done without the use of a Legendre transformation, (4) the Koopman-von Neumann theory is obtained as a result of our ab initio operational approach, (5) previous work on the Schwinger action principle for classical systems is generalized to include holonomic constraints.
