Precession on a rotating saddle: a gyro force in an inertial frame

Particles in rotating saddle potentials exhibit precessional motion which, up to now, has been explained by explicit computation. We show that this precession is due to a hidden gyroscopic force which, unlike the standard Coriolis force, is present in the inertial frame. We do so by finding a hodograph-like “guiding center” transformation using the method of normal form, which yields a simplified equation for the guiding center of the trajectory that coincides with the equation of the Foucault’s pendulum. In this sense, a particle trapped in the symmetric rotating saddle trap is, effectively, a Foucault’s pendulum, but in the inertial frame.