  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 Panth\'eon (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.
