Abstract
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.
Citation
Daniela Emmanuele. Marcos Salvai. "Force Free Möbius Motions of the Circle." J. Geom. Symmetry Phys. 27 59 - 65, 2012. https://doi.org/10.7546/jgsp-27-2012-59-65
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