Force free Moebius motions of the circle

DANIELA EMMANUELE; MARCOS SALVAI

Journal of Geometry and Symmetry in Physics

Academia Búlgara de Ciencias

Lugar: Sofía; Año: 2012 vol. 27 p. 59 - 65

1312-5192

Let 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 congurations differ in an element of M. We describe all force free Möbius motions, that is, those curves in M which are critical points of the kinetic energy. The main tool is a Riemannian metric on M which turns out to be not complete (in particular not invariant, as happens with non-rigid motions) given by the kinetic energy.