Dynamical symmetries of the geodesic equation
type: Item
instance of: scholarly article
title: Dynamical symmetries of the geodesic equation
zbMATH Open document ID: 0563.70015
DOI: 10.1007/BF02080551
author: Giacomo Caviglia
published in: International Journal of Theoretical Physics
publication date: 1983-01-01T00:00:00Z
review text: A class of dynamical symmetries for the Euler-Lagrange equations with the Lagrangian \(L=(1/2)g_{ab}\dot q^ a\dot q^ b\) is determined \((g_{ab}\) are components of Riemannian metric). This class consists of symmetries such that their natural projection onto the configuration manifold yields a vector field or is generated by a totally symmetric tensor field. As it has been recently shown, in general relativity such objects may play the role of generators of the first-integrals of geodesic motion. It is shown in this paper, that the class of tensor fields associated with dynamical symmetries coincides with the family of generalized Killing tensors. Generation of new first integrals through the deformation of a given one via a dynamical symmetry is examined. Correspondent Noether-type conserved quantities are also explicitly exhibited.
Mathematics Subject Classification ID: 70G45
zbMATH DE Number: 3898293
zbMATH Keywords: dynamical symmetries
zbMATH Keywords: Euler-Lagrange equations
zbMATH Keywords: first-integrals of geodesic motion
zbMATH Keywords: generalized Killing tensors
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3898293