Killing pairs and Newtonian integrals of motion
type: Item
instance of: scholarly article
title: Killing pairs and Newtonian integrals of motion
zbMATH Open document ID: 0532.70010
DOI: 10.1007/BF00403272
author: Basilis C. Xanthopoulos
published in: Letters in Mathematical Physics
publication date: 1982-01-01T00:00:00Z
review text: Killing pairs of symmetric tensor fields on a Riemannian manifold M describe integrals of the geodesics which are rational functions in the velocity coordinates. A well-known theorem of analytical mechanics states, that the orbits of a conservative Newtonian system, given by a Riemannian manifold (M,g) and a potential function V, which have energy E, can be parametrized such that they are normalized geodesics of the metric (E-V)g. The Killing pairs with respect to this metric therefore give integrals of the Newtonian motion, which are rational functions in the velocities. This allows a configuration space description of the integrals, closely parallel to the usual phase space formulation. The use of the configuration space language has attractive aspects in view of the intrinsic algebraic structure of the set of pairs of symmetric tensor fields.
Mathematics Subject Classification ID: 70G45
Mathematics Subject Classification ID: 70G10
Mathematics Subject Classification ID: 70F20
zbMATH DE Number: 3845106
zbMATH Keywords: integrals of geodesics
zbMATH Keywords: rational functions in velocity coordinates
zbMATH Keywords: orbits of conservative Newtonian system
zbMATH Keywords: configuration space description of integrals
zbMATH Keywords: Killing pairs of symmetric tensor fields
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: potential function
reviewed by: Klaus Horneffer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3845106