论文标题
无处不在的洛伦兹力量
The Ubiquitous Lorentz Force
论文作者
论文摘要
最大程度地减少拉格朗日的动作积分，可在拉格朗日力学的优雅机械中提供Euler-Lagrange运动方程。但是，两个关系定义了当前和能量摩托车的差异，并为Euler-Lagrange方程提供了另一种动机，而无需调用最小动作原理所需的相当大的机械。这两个关系的推导仅在拉格朗日对当地差异操作进行，而没有定义行动的全球整合。这两种关系连接了当前的局部连续性方程（作为消失的差异）和能量摩托车与洛伦兹力，对称性和Euler-Lagrange方程。 Euler-Lagrange方程都是两种关系的共同点，因此为运动方程式提供了足够的动力。能量摩托车，力，电流，对称和运动方程的中心概念之间的基本关系提供了教学上有趣的清晰度。学生将看到这些概念如何相互关系以及每个概念的定义。
Minimizing the Action integral of a Lagrangian provides the Euler-Lagrange equation of motion in the elegant machinery of Lagrangian Mechanics. However two relations define the divergence of current and energy-momentum, and provide an alternative motivation for the Euler-Lagrange equation without invoking the considerable machinery required for the principle of least Action. The derivation of these two relations proceeds with only local differential operations on the Lagrangian, and without a global integration defining an Action. The two relations connect local continuity equations (as a vanishing divergence) for current and energy-momentum to Lorentz force, symmetry, and the Euler-Lagrange equation. The Euler-Lagrange equation is common to both relations so providing sufficient motivation for acceptance as equations of motion. The essential relationships between the central concepts of energy-momentum, force, current, symmetry and equation of motion provide pedagogically interesting clarity. The student will see that how these concepts relate to each other as well as the definition of each concept in isolation.
