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We calculate exactly the modes of motion of the Time-averaged OrbitingPotential (TOP) trap with its four degrees of freedom, namely the threetranslations and the spin, taken into account. We find that, when gravity isneglected, there are two parameters in the problem namely, the angular velocityof the rotating field and its strength. We present the stability diagram inthese parameters. We find the mode frequencies calculated from thetime-averaged potential model used by the inventors of the TOP is an excellentapproximation to our exact results. However, for other parameters, this may notbe the case.Comment: 18 pages, 1 EPS figur

Dynamic stability of the time-averaged orbiting potential trap: Exact classical analysis