Dynamical invariants of rigid motions on the hyperbolic plane
type: Item
instance of: scholarly article
title: Dynamical invariants of rigid motions on the hyperbolic plane
zbMATH Open document ID: 0723.53008
DOI: 10.1007/BF00147409
author: Péter T. Nagy
published in: Geometriae Dedicata
publication date: 1991-01-01T00:00:00Z
review text: Let \({\mathcal H}^ 2\) be a hyperbolic plane. A particle \(\{\) P,m\(\}\) is a pair given by a point \(P\in {\mathcal H}^ 2\) and a positive real number m; they are called the center and mass of the particle. A rigid particle system \(\{P_ k,m_ k\}^ n_{k=1}\) (n\(\geq 2)\) is a finite set of particles with given distances \(d(P_ i,P_ j)\), \(i,j=1,2,...,n\), of centers. It is well known that the only dynamical invariants of a rigid particle system on a Euclidean plane are the mass center and the ratio of mass and inertia. This means that these data and the initial position and velocity determine uniquely the force-free motion. The situation is much more complicated on the hyperbolic plane. This paper is devoted to the investigation of the geometry of left invariant metrics on the isometry group of the hyperbolic plane determined by the kinetic energy of a rigid particle system.
Mathematics Subject Classification ID: 53A35
Mathematics Subject Classification ID: 53B50
Mathematics Subject Classification ID: 70F10
zbMATH DE Number: 4192544
zbMATH Keywords: dynamical invariants
zbMATH Keywords: rigid particle system
zbMATH Keywords: hyperbolic plane
zbMATH Keywords: left invariant metrics
zbMATH Keywords: isometry group
zbMATH Keywords: kinetic energy
reviewed by: Zdeněk Jankovský
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4192544