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The anisosphere model : a novel differential phase space representation for Foucault pendulums and 2D oscillators

Verreault René. (2018). The anisosphere model : a novel differential phase space representation for Foucault pendulums and 2D oscillators. Journal of Physics : Conference Series, 1141, p. 1-14.

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URL officielle: https://dx.doi.org/doi:10.1088/1742-6596/1141/1/01...

Résumé

: It is customary to describe the behaviour and stability of oscillators with the help of phase space representation. However, two-dimensional (2D) oscillators like the Foucault pendulum call for a 4D phase space that is not simple to visualize. Applying celestial body perturbation theory to the Foucault pendulum in his doctor dissertation, Nobel laureate Kamerlingh Onnes showed that the essential features of a Foucault pendulum are its inherent circular and linear anisotropies. A spherical differential 2D sub-space can be defined, where the group of the points of a spherical surface with respect to the operation rotation about a diametral axis is isomorphic with the group of sequential states of oscillation of a 2D pendulum with respect to the operation translation in time . Any Foucault pendulum is then characterized by two elliptical eigenstates which are represented by the poles of that rotation axis on the so-called anisosphere. Such poles play the role of attractor/repellor when “dichroic” damping is present. Moreover, they move drastically within a meridian plane when nonlinear restoring torque giving rise to Airy precession occurs. The concept of anisosphere constitutes a very powerful tool for analysing and optimizing actual Foucault pendulum implementations. That feature is illustrated by a numerical model.

Type de document:Article publié dans une revue avec comité d'évaluation
ISSN:1742-6588
Volume:1141
Pages:p. 1-14
Version évaluée par les pairs:Oui
Date:2018
Identifiant unique:10.1088/1742-6596/1141/1/012063
Sujets:Sciences naturelles et génie > Sciences naturelles > Astronomie et astrophysique
Sciences naturelles et génie > Sciences naturelles > Physique
Département, module, service et unité de recherche:Départements et modules > Département des sciences fondamentales
Mots-clés:anisosphere model, Foucault pendulum, linear anisotropy
Informations complémentaires:Proceedings of International Conference on Mathematical Modelling in Physical Sciences 27–31 October 2018, Moscow, Russian Federation
Déposé le:15 mai 2020 12:55
Dernière modification:15 mai 2020 12:55
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