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单词 Principle of least action
释义

Principle of least action

中文百科

最小作用量原理

光线从点Q传播至点O时,会被半圆形或混合形镜子反射,最终抵达点P。
光线从点Q传播至点O时,会被混合形状镜子反射,最终抵达点P。
光线从介质1的点Q,在点O移动进入介质2,发生折射,最后抵达介质2的点P。

在物理学里,最小作用量原理英语:least action principle),或更精确地,平稳作用量原理英语:stationary action principle),是一种变分原理,当应用于一个机械系统的作用量时,可以得到此机械系统的运动方程序。这原理的研究引导出经典力学的拉格朗日表述和哈密顿表述的发展。卡尔·雅可比特称最小作用量原理为分析力学之母。

在现代物理学里,这原理非常重要,在相对论、量子力学、量子场论里,都有广泛的用途。在现代数学里,这原理是莫尔斯理论的研究焦点。本篇文章主要是在阐述最小作用量原理的历史发展。关于数学描述、推导和实用方法,请参阅条目作用量。最小作用量原理有很多种例子,主要的例子是莫佩尔蒂原理(Maupertuis' principle)和哈密顿原理。

英语百科

Principle of least action 最小作用量原理

As the system evolves, q traces a path through configuration space (only some are shown). The path taken by the system (red) has a stationary action (δS = 0) under small changes in the configuration of the system (δq).[10]
This article discusses the history of the principle of least action. For the application, please refer to action (physics).

The principle of least action – or, more accurately, the principle of stationary action – is a variational principle that, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system. In relativity, a different action must be minimized or maximized. The principle can be used to derive Newtonian, Lagrangian, Hamiltonian equations of motion, and even General Relativity. It was historically called "least" because its solution requires finding the path that has the least change from nearby paths. Its classical mechanics and electromagnetic expressions are a consequence of quantum mechanics, but the stationary action method helped in the development of quantum mechanics.

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更新时间:2025/6/17 4:55:22