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Open AccessArticle

The Formulations of Classical Mechanics with Foucault’s Pendulum

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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
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Service de Physique Nucléaire et Subnucléaire, Université de Mons—UMONS, Research Institute for Complex Systems, Place du Parc 20, 7000 Mons, Belgium; CeREF, HELHa, Chaussée de Binche 159, 7000 Mons, Belgium
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Author to whom correspondence should be addressed.
Physics 2020, 2(4), 531-540; https://doi.org/10.3390/physics2040030
Received: 2 September 2020 / Revised: 25 September 2020 / Accepted: 25 September 2020 / Published: 1 October 2020
(This article belongs to the Section Physics Education)
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. View Full-Text
Keywords: classical mechanics; Foucault’s pendulum; Hamiltonian formalism; action-angle variables classical mechanics; Foucault’s pendulum; Hamiltonian formalism; action-angle variables
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Boulanger, N.; Buisseret, F. The Formulations of Classical Mechanics with Foucault’s Pendulum. Physics 2020, 2, 531-540.

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