Journal of Geometry and Symmetry in Physics

Force Free Möbius Motions of the Circle

Daniela Emmanuele and Marcos Salvai

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Let $\mathcal{M}$ be the Lie group of Möbius transformations of the circle. Suppose that the circle has initially a homogeneous distribution of mass and that the particles are allowed to move only in such a way that two configurations differ in an element of $\mathcal{M}$. We describe all force free Möbius motions, that is, those curves in $\mathcal{M}$ which are critical points of the kinetic energy. The main tool is a Riemannian metric on $\mathcal{M}$ which turns out to be not complete (in particular not invariant, as happens with non-rigid motions) given by the kinetic energy.

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J. Geom. Symmetry Phys., Volume 27 (2012), 59-65.

First available in Project Euclid: 26 May 2017

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Emmanuele, Daniela; Salvai, Marcos. Force Free Möbius Motions of the Circle. J. Geom. Symmetry Phys. 27 (2012), 59--65. doi:10.7546/jgsp-27-2012-59-65.

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