## Journal of Geometry and Symmetry in Physics

### Force Free Möbius Motions of the Circle

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 26 May 2017

https://projecteuclid.org/euclid.jgsp/1495764128

Digital Object Identifier
doi:10.7546/jgsp-27-2012-59-65

Mathematical Reviews number (MathSciNet)
MR3026387

Zentralblatt MATH identifier
1267.53016

#### Citation

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. https://projecteuclid.org/euclid.jgsp/1495764128