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


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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Daniela Emmanuele. Marcos Salvai. "Force Free Möbius Motions of the Circle." J. Geom. Symmetry Phys. 27 59 - 65, 2012.


Published: 2012
First available in Project Euclid: 26 May 2017

zbMATH: 1267.53016
MathSciNet: MR3026387
Digital Object Identifier: 10.7546/jgsp-27-2012-59-65

Rights: Copyright © 2012 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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