Two often disregarded aspects of Foucault's pendulum

This paper revisits the famous Foucault's pendulum by highlighting two often-disregarded aspects in mechanics courses. The first one concerns the existence of a local accelerated reference frame to express the law of dynamics without the Coriolis force. The second aspect deals with the geometrical phase that appears in pendulum dynamics. This last point, which could appear banal, should be related to analogous consideration in quantum physics. It is also linked to vectorial parallel transport of the pendulum angular momentum eigenvector. Numerical simulations with MATLAB are proposed. (paper)