爱丽丝和福柯摆：action -角度变量的土地
Alice and the Foucault Pendulum: the land of action-angle variables
摘要：
自从牛顿$(1643-1727)$的开创性工作以来，力学一直在不断地重塑自己：特别是拉格朗日$(1736-1813)$和汉密尔顿$(1805-1865)$，它现在为探索最复杂的动力系统提供了强大的概念和数学工具，基本上是通过作用角变量公式化，更普遍地通过正则变换理论。我们给读者一个概述这些不同的配方通过著名的例子福柯的钟摆，一个设备创建的福柯$(1819-1868)$和第一次安装在先贤祠（巴黎，法国）在1851年显示地球的旋转。福柯摆的表面上的简单性实际上是通向经典力学最当代分支的一扇敞开的大门。我们强调，作用角变量形式主义是没有必要了解福柯的钟摆。后者被简单地视为众所周知的简单动力系统，用于解释现代概念，这些概念对于理解更复杂的动力系统至关重要。福柯摆安装在学院教堂的Sainte-Waudru（蒙斯，比利时）将使我们能够数值估计不同的数量介绍。一个自由改编的摘录从“爱丽丝梦游仙境”将提供读者一些诗意的呼吸。
英文摘要：
Since the pioneering works of Newton $(1643-1727)$, Mechanics has been constantly reinventing itself: reformulated in particular by Lagrange $(1736-1813)$ then Hamilton $(1805-1865)$, it now offers powerful conceptual and mathematical tools for the exploration of the most complex dynamical systems, essentially via the action-angle variables formulation and more generally through the theory of canonical transformations. We give the reader an overview of these different formulations through the well-known example of Foucault's pendulum, a device created by Foucault $(1819-1868)$ and first installed in the Panthéon (Paris, France) in 1851 to display the Earth's rotation. The apparent simplicity of the Foucault pendulum is indeed an open door to the most contemporary ramifications of Classical Mechanics. We stress that the action-angle variable formalism is not necessary to understand Foucault's pendulum. The latter is simply taken as well-known simple dynamical system used to exemplify modern concepts that are crucial in order to understand more complicated dynamical systems. The Foucault pendulum installed in the collegiate church of Sainte-Waudru (Mons, Belgium) will allow us to numerically estimate the different quantities introduced. A free adaptation of excerpts from "Alice's Adventures in Wonderland" will offer the reader some poetic breaths.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
