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The Formulations of Classical Mechanics with Foucault’s Pendulum

dc.rights.licenseCC1en_US
dc.contributor.authorBUISSERET, Fabien
dc.contributor.authorBoulanger, Nicolas
dc.date.accessioned2020-10-07T11:40:13Z
dc.date.available2020-10-07T11:40:13Z
dc.date.issued2020-10-01
dc.identifier.urihttps://luck.synhera.be/handle/123456789/330
dc.identifier.doi10.3390/physics2040030en_US
dc.description.abstractSince 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.en_US
dc.description.abstractenSince 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.en_US
dc.description.sponsorshipNoneen_US
dc.language.isoENen_US
dc.publisherMDPIen_US
dc.relation.ispartofPhysicsen_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.subjectMécaniqueen_US
dc.subjectPenduleen_US
dc.subjectVariables d'action-angleen_US
dc.subjectTransport parallèleen_US
dc.titleThe Formulations of Classical Mechanics with Foucault’s Pendulumen_US
dc.typeArticle scientifiqueen_US
synhera.classificationPhysique, chimie, mathématiques & sciences de la terreen_US
synhera.institutionCERDECAMen_US
synhera.otherinstitutionHELHaen_US
synhera.otherinstitutionUMONSen_US
synhera.cost.total830en_US
synhera.cost.apc830en_US
synhera.cost.comp0en_US
synhera.cost.acccomp0en_US
dc.description.versionOuien_US
dc.rights.holderMDPIen_US


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