A Coriolis 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 Coriolis-like 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. We also point out that the transformation cannot be of contact type in principle, thus showing that the standard (in applied literature) heuristic averaging gives the correct result but obscures the fact that the transformation of the position must involve the velocity.