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Slow manifold and Hannay angle in the spinning top

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Translated title of the contributionSlow manifold and Hannay angle in the spinning top
Original languageEnglish
Pages (from-to)115 - 127
Number of pages13
JournalEuropean Journal of Physics
Volume32
DOIs
DatePublished - Jan 2011

Abstract

The spin of a top can be regarded as a fast variable, coupled to the motion of the axis which is slow. In pure precession, the rotation of the axis round a cone (without nutation), can be considered as the result of a reaction from the fast spin. The resulting restriction of the total state space of the top is an illustrative example, at graduate-student level, of the general dynamical concept of the slow manifold. For this case, the slow manifold can be calculated exactly, and expanded as a series of reaction forces (of magnetic type) in powers of slowness, corresponding to a modified precession frequency. The forces correspond to a series for the Hannay angle for the fast motion, describing the location of a point on the top.

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