The Formulations of Classical Mechanics with Foucault’s Pendulum

Since the pioneering works of Newton (1643&ndash
1727), Mechanics has been constantly reinventing itself: reformulated in particular by Lagrange (1736&ndash
1813) then Hamilton (1805&ndash
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&rsquo
s pendulum, a device created by Foucault (1819&ndash
1868) and first installed in the Panth&eacute
on (Paris, France) in 1851 to display the Earth&rsquo
s rotation. The apparent simplicity of Foucault&rsquo
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&rsquo
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&rsquo
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.