The Formulations of Classical Mechanics with Foucault’s Pendulum

Physics

Fabien Buisseret¹  Nicolas Boulanger² 

[1] Service de Physique Nucléaire et Subnucléaire, Université de Mons—UMONS, Research Institute for Complex Systems, Place du Parc 20, 7000 Mons, Belgium;Service de Physique de l’Univers, Champs et Gravitation, Université de Mons—UMONS, Research Institute for Complex Systems, Place du Parc 20, 7000 Mons, Belgium;

关键词: classical mechanics;    Foucault’s pendulum;    Hamiltonian formalism;    action-angle variables;   

DOI  :  10.3390/physics2040030

来源: DOAJ

【 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 dynamical systems, essentially via the action-angle variables formulation and more generally through the theory of canonical transformations. We propose to the (graduate) 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 Foucault’s pendulum is indeed an open door to the most contemporary ramifications of classical mechanics. We stress that adopting the formalism of action-angle variables is not necessary to understand the dynamics of Foucault’s pendulum. The latter is simply taken as well-known and simple dynamical system used to exemplify and illustrate modern concepts that are crucial in order to understand more complicated dynamical systems. The Foucault’s pendulum first installed in 2005 in the collegiate church of Sainte-Waudru (Mons, Belgium) will allow us to numerically estimate the different quantities introduced.

【 授权许可】

Unknown