Levitating a spinning magnetic top above an air coil

Gov, S.; Matzner, H.; Shtrikman, S.

doi:10.1109/eeis.1996.567007

Cited by 2 publications

(5 citation statements)

References 3 publications

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“…Since the tolerance on the weight is about 2% (see Ref. [10]) it follows that θ * 0 ∼ 0.1rad. Although we did not measure ∆ directly, our experiments, including those in which we have artificially changed ∆ indicate that ∆/θ * 0 ≪ 1.…”

Section: Equilibrium Considerationsmentioning

confidence: 99%

“…How the trap works in the quantum regime? and other questions have been studied recently [6,7,8,9,10,11] whereas other questions such as how does friction affect the stability of the top are currently under study.…”

Section: The Hovering Magnetic Topmentioning

confidence: 99%

“…To estimate θ * 0 we recall that the tolernace on the weight is equal to the toleance allowed on the lift. It follows that [10]…”

Section: Equilibrium Considerationsmentioning

confidence: 99%

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On the spinning motion of the hovering magnetic top

Flanders

Gov

Shtrikman

et al. 1999

Physica D: Nonlinear Phenomena

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In this paper we analyze the spinning motion of the hovering magnetic top. We have observed that its motion looks different from that of a classical top. A classical top rotates about its own axis which precesses around a vertical fixed external axis. The hovering magnetic top, on the other hand, has its axis slightly tilted and moves rigidly * Also with the Department of Physics, University of California, San Diego, La Jolla, 92093 CA, USA 1 as a whole about the vertical axis. We call this motion synchronous, because in a stroboscopic experiment we see that a point at the rim of the top moves synchronously with the top axis.We show that the synchronous motion may be attributed to a small deviation of the magnetic moment from the symmetry axis of the top. We show that as a consequence, the minimum angular velocity required for stability is given by 4µHI 1 /I 2 3 for I 3 > I 1 and by µH/(I 3 − I 1 ) for I 3 < I 1 . Here, I 3 and I 1 are the principal and secondary moments of inertia, µ is the magnetic moment, and H is the magnetic field. For comparison, the minimum angular for a classical top is given by 4µHI 1 /I 2 3 both for I 3 < I 1 and for I 3 > I 1 . We also give experimental results that were taken with a top whose moment of inertia I 1 can be changed. These results show very good agreement with our calculations.

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Section: Equilibrium Considerationsmentioning

confidence: 99%

Section: The Hovering Magnetic Topmentioning

confidence: 99%

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On the spinning motion of the hovering magnetic top

Flanders

Gov

Shtrikman

et al. 1999

Physica D: Nonlinear Phenomena

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“…Note, however, that the lower mass region (of less than 0.818m 0 ) is difficult to access. Also, the top retains a finite kinetic energy when launched into the trap which, as has been discussed by us [13], further decreases the mass tolerance in practice. Last but not least, the theoretical mass tolerance, given in Eq.…”

Section: Solution For the Equations Of Motionmentioning

confidence: 87%

“…The physical principle underlying the operation of the hovering magnetic top relies on the so-called 'adiabatic approximation' [4,5,6,7]: As the top is launched, its magnetization points antiparallel to the magnetization of the base in order to supply the repulsive magnetic force which will act against the gravitational pull. As the top hovers, it experiences lateral oscillations which are slow ( Ω lateral ≃ 1Hz) compared to its precession (Ω precession ∼ 5Hz).…”

Section: Qualitative Descriptionmentioning

confidence: 99%

On the dynamical stability of the hovering magnetic top

Gov

Shtrikman

Thomas

1999

Physica D: Nonlinear Phenomena

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In this paper we analyze the dynamic stability of the hovering magnetic top from first principles without using any preliminary assumptions. We write down the equations of motion for all six degrees of freedom and solve them analytically around the equilibrium solution. Using this solution we then find conditions which the height of the hovering top above the base, its total mass, and its spinning speed have to satisfy for stable hovering.The calculation presented in this paper can be used as a guide to the analysis and synthesis of magnetic traps for neutral particles.

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Levitating a spinning magnetic top above an air coil

Cited by 2 publications

References 3 publications

On the spinning motion of the hovering magnetic top

On the spinning motion of the hovering magnetic top

On the dynamical stability of the hovering magnetic top

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