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

Abstract eng:
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 stande 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.

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