On the dynamical stability of the hovering magnetic top

The Levitron is a toy that consists of a spinning top that levitates over a magnetic base for a few minutes, until air drag decreases the spin rate below a certain limit. Stable levitation, lasting hours or even days, has been achieved for Levitrons that were externally driven by either an air jet or an alternating magnetic field. We report measurements of stable levitation for the latter case. We show that the top precession couples with the frequency of the alternating field, so that the precession period equals the period of the field. In addition, the top rotates around itself with the same period. We present numerical simulations that reproduce the essential features of this dynamics. It is also shown that the magnetic torque that drives the top is due to a misalignment between the magnetic dipole moment and the mechanical axis of the top.

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“…The second prediction by Simon et al, which is also made by other authors, 5,6 is that the top oscillates in z with a frequency…”

mentioning

confidence: 61%

“…2, [4][5][6][7][8] Once the top is in a stable state of levitation, air friction eventually decreases the spin rate. After about 2 min, the angular velocity drops below the lower stability limit and the levitation ends.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Levitron under a periodic magnetic forcing

Pérez

García-Sánchez

2015

American Journal of Physics

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“…In our approach, based on [5], these two motions (precession and nutation) are ignored (orientational stability is considered as given), whereas assumptions are made about the top orientation during excursions around the equilibrium position. More sophisticated models, which account for the complex dynamics of the Levitron c , are available in the literature [4,6,8,9].…”

Section: 2 Stability Analysismentioning

confidence: 99%

“…Mechanical aspects are not addressed in this study: the impact of top rotation speed against stability is for instance not discussed. However, the authors are convinced that this approach can be used as a base for the comprehension of the complex phenomenology of the Levitron c , and suggest references [4,6,8,9] for more detailed models. …”

Section: Introductionmentioning

confidence: 99%

Gyroscopic magnetic levitation: an original design procedure based on the finite element method

Grève

Versele

Lobry

2010

Eur. Phys. J. Appl. Phys.

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To cite this version:Z. De Grève, C. Versèle, J. Lobry. Gyroscopic magnetic levitation: an original design procedure based on the finite element method. European Physical Journal: Applied Physics, EDP Sciences, 2010, 52 (2), <10.1051/epjap/2010080>. Abstract. In this work, an original procedure, based on the finite element method, is presented for the design of a Levitron c , a device made of permanent magnets and relying on stable gyroscopic magnetic levitation, using secondhand components. A perturbation force analysis is performed on finite element models of available magnets in order to derive the locus of stable equilibrium, as well as the top mass, for a given configuration of the magnets. We investigate three methods for the estimation of forces from finite element computations, two of them based on the virtual work principle, and one performing numerical integration of the classical expression of forces between magnets. Results are employed to realize a Levitron c in laboratory, and are shown to be in better agreement with experience than those from a simple analytical model available in the literature.

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“…However, it requires power, interacts detrimentally with spacecraft electronics, induces unwanted, attitudeperturbing torques due to surrounding fi elds (such as the geomagnetic fi eld), and introduces the very real risk that a temporary loss of power or a software failure may cause the assembly to lose structural integrity.  Oscillating and moving magnets, whose quasipassive, periodic motion creates relative equilibria (in the Hamiltonian sense): An entertaining example of this behavior is popular Levitron toy (Gov et al 1999(Gov et al , 2000, in which one spinning magnet levitates several inches above another. Because it depends on bound angular momentum, this principle is not particularly useful for spacecraft, where angular momentum is carefully managed for attitude control.…”

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confidence: 99%

Non-Contacting Interfaces: A Case Study in Modular Spacecraft Design

Butail¹,

Peck²

2007

Syst. Res. Forum

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The benefi ts of modularization, such as reusability and upgradeability, remain underutilized in space. Exploiting these advantages after a spacecraft is launched introduces too much cost and risk in the current paradigm of spacesystem design. This gap between modular design and its benefi ts has inspired us to focus attention on interfaces. Many of the obstacles to bridging this gap lie in mechanical attachment of spacecraft subsystems. This paper reexamines the function of mechanical interfaces among spacecraft components and describes a new realization in which fl ux-pinning superconductors and permanent magnets provide stable, but unpowered, connections among spacecraft components that appear to hover at some distance from one another. Beginning with functional abstraction, this study identifi es a new set of unexploited possibilities that add versatility to space-systems architectures. First, the limitations imposed on modularity due to mechanical coupling in spacecraft architecture are identifi ed. These limitations are then used to back out the requirements for a non-contacting interface. With several technologies that enable adhesion without mechanical contact identifi ed, requirements fl owdown and functional analysis is performed to quantify technical performance measures for the interface.

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On the dynamical stability of the hovering magnetic top

Cited by 18 publications

References 9 publications

Dynamics of a Levitron under a periodic magnetic forcing

Dynamics of a Levitron under a periodic magnetic forcing

Gyroscopic magnetic levitation: an original design procedure based on the finite element method

Non-Contacting Interfaces: A Case Study in Modular Spacecraft Design

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