Jacobi method and the eikonal equation
type: Item
instance of: scholarly article
title: Jacobi method and the eikonal equation
zbMATH Open document ID: 0899.35017
DOI: 10.1007/BF02404085
author: I. S. Emel'yanova
published in: Computational Mathematics and Modeling
publication date: 1998-08-26T00:00:00Z
review text: The first part of the paper contains a discussion of the analogy between the Hamilton-Jacobi equation modelling the rotation of a rigid body around a fixed point and some variants of the eikonal equation in optics. Next, a survey of the best known integrability cases (Euler's, Lagrange's, Kowalevskaya's, Delone's, Hess') of the equation of a rotating rigid body is presented. The last part of the paper concerns the so called ``group analysis'' of the canonical differential system associated to a smooth Hamiltonian where the following Proposition is proved: ``The Hamiltonian symmetry leading to the construction of an integral of the canonical equations is in general not a dynamical symmetry''.
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 35A25
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 58J70
zbMATH DE Number: 1188583
zbMATH Keywords: Hamilton-Jacobi equation
zbMATH Keywords: canonical system
zbMATH Keywords: rotation of a rigid body
zbMATH Keywords: integrability cases
reviewed by: Ştefan Mirică
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02404085
OpenAlex ID: W1972138910
description: scientific article; zbMATH DE number 1188583