Non inertial dynamics and holonomy on the ellipsoid

Traditionally, the discussion about the geometrical interpretation of inertial forces is reserved for General Relativity handbooks. In these notes an analysis of the effect of such forces in a classical (newtonian) context is made, as well as a study of the relation between the precession of the Foucault pendulum and the holonomy on a surface, including some critical remarks about the common statement \textquotedblleft precession of Foucault pendulum equals holonomy on the sphere\textquotedblright.