ICCM Conferences, The 5th International Conference on Computational Methods (ICCM2014)

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Keynote: Levitron: an exotic toy of nonlinear and linearised dynamics
Elvio Bonisoli

Last modified: 2014-07-14

Abstract


The Levitron is a revolutionary toy that continues to astonish beginners and experts of spinning tops. Permanent magnets demonstrate experimentally that can levitate practically without any dissipative effects in the air, but the complexity of the dynamic equations of this famous and exotic toy are relevant. In particular the stability region and the related boundary conditions are  surprising and a single model shows difficulties to be consistent for all kind of its dynamics. The paper presents an unique nonlinear magneto-rotordynamic model that allows obtaining the nonlinear equations of motion of all rigid body modes of the Levitron, and with which it is possible to describe the complete dynamic behaviour of the spinning top and to highlight the presence of stability fields related to its spin speed and vertical position of levitation. The developed model takes into account also the effect of the aerodynamic drag torque on the sides of the spinning top. The advantage of this unique model is also its property to describe and to underline the intrinsic linearised and nonlinear dynamics and the capabilities of this exotic toy to extend the characteristic of a nonlinear system dependent on large displacements and spin speed. To experimentally identify the complex dynamic behaviour of the spinning top, an experimental investigation has been developed on a dedicated test bench and some tests are discussed. By means of the numerical integration of the equations of motion, the spatial trajectories of the spinning top have been computed and validated by comparison with the experimental test results.


Keywords


modeling, simulation

References


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