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

http://cims.nyu.edu/ams/abstracts/kirillov

PRECESSION ON A ROTATING SADDLE: A GYRO FORCE IN AN INERTIAL FRAME
Oleg Kirillov, Steklov Mathematical Institute, Moscow and Helmholtz-Zentrum, Dresden-Rossendorf

Abstract:

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. This is a joint work with Mark Levi (Penn State).