The generalized Maupertuis principle
type: Item
instance of: scholarly article
title: The generalized Maupertuis principle
zbMATH Open document ID: 0941.70014
author: K. Appert
published in: Regular and Chaotic Dynamics
publication date: 2000-07-26T00:00:00Z
review text: For a Lagrangian of type \(L=T-V\), where the kinetic energy function \(T\) comes from a Riemannian metric \(g\), the classical Maupertuis principle states that trajectories with total energy \(E\) are geodesics of the Jacobi metric \(g_E = 2(E-V)g\) (at least on the ``admissible configuration space'' determined by \(V<E\)). Here the author discusses the generalized situation where the metric can have e.g. Lorentzian signature, and the Jacobi metric is taken as \(g_E = 2|E-V|g\). He proves existence and uniqueness of geodesics of \(g_E\) passing through the singular boundary where \(|E-V|=0\). The main theorem states that trajectories of the system with Lagrangian \(L\) are pregeodesics of \(g_E\), carrying a number of isolated points on the singular boundary or a number of line segments and isolated points. This extension of the Maupertuis principle is relevant for applications in general relativity.
reviewed by: W. Sarlet
Mathematics Subject Classification ID: 70H30
Mathematics Subject Classification ID: 70H40
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 70G45
Mathematics Subject Classification ID: 49S05
zbMATH DE Number: 1281654
zbMATH Keywords: Maupertuis principle
zbMATH Keywords: non-Riemannian metrics
zbMATH Keywords: relativistic mechanics
zbMATH Keywords: Lagrangian
zbMATH Keywords: geodesics
zbMATH Keywords: Jacobi metric
zbMATH Keywords: Lorentzian signature
zbMATH Keywords: existence and uniqueness of geodesics
zbMATH Keywords: singular boundary
zbMATH Keywords: pregeodesics
MaRDI profile type: Publication
full work available at URL: rd1998v003n02abeh000067
OpenAlex ID: W4241202515
DOI: 10.1070/RD1998V003N02ABEH000067
description: scientific article; zbMATH DE number 1281654