Nonstandard variational calculus with applications to classical mechanics. I: An existence criterion
type: Item
instance of: scholarly article
title: Nonstandard variational calculus with applications to classical mechanics. I: An existence criterion
zbMATH Open document ID: 0937.49010
DOI: 10.1023/A:1026661620598
author: Fabio Bagarello
published in: International Journal of Theoretical Physics
publication date: 1999-11-18T00:00:00Z
review text: This is Part I of an excellent two part paper that applies Robinson-styled nonstandard analysis to the variational calculus and applications. In this first of two successive parts in the same journal (see also the following review of Part II), the author finds a discretized version of the Euler-Lagrange equation for classical dynamical systems and discusses the existence of an extremum for a given functional in variational calculus. Some results related to the Cauchy existence theorem are obtained and this is coupled with a discussion for various examples.
Mathematics Subject Classification ID: 49J99
Mathematics Subject Classification ID: 03H05
Mathematics Subject Classification ID: 03H10
Mathematics Subject Classification ID: 58E30
Mathematics Subject Classification ID: 70H30
zbMATH DE Number: 1364373
zbMATH Keywords: nonstandard analysis
zbMATH Keywords: variational methods
zbMATH Keywords: Euler-Lagrange equation
MaRDI profile type: Publication
full work available at URL: a:1026661620598
OpenAlex ID: W245348235
description: scientific article; zbMATH DE number 1364373