Geometric control approach for the Foucault pendulum
Felipe Monroy-Perez, Alfonso Anzaldo-Meneses
Non-linear control systems defined by means of a distribution of smooth vector fields are relevant because provide good models for nonholonomic systems in mechanics, automation and classical particle physics.
In this paper we approach the classical Foucault pendulum, which is accepted as indisputable demonstration of the Earth rotation movement, through the formalism of geometric control theory. By applying the Pontryagin Maximum Principle, we derive some geometric properties for trajectories for the particular case of small oscillations, and establish the link to the well known Hopf fibration.