Group classification for path equation describing minimum drag work and symmetry reductions
type: Item
instance of: scholarly article
title: Group classification for path equation describing minimum drag work and symmetry reductions
zbMATH Open document ID: 1223.34054
author: Mehmet Pakdemirli
author: Yiğit Aksoy
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2010-11-23T00:00:00Z
review text: The authors apply the symmetry group method to the path equation which describes the minimum drag work earlier proposed by the first author [``The drag work minimization path for a flying object with altitude-dependent drag parameters'', Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science 223, No.~5, 1113--1116 (2009)]. They perform a Lie group classification with respect to the altitude dependent function. Various cases arise for which extensions of the principal Lie algebra are necessary. Cases which admit the maximal eight symmetries are significant. The symmetries obtained are used in two ways: (i) some group-invariant solutions are deduced and (ii) canonical coordinates are invoked to reduce the order of the equation. This contribution will appeal to those working in symmetries of ordinary differential equations and its applications.
Mathematics Subject Classification ID: 34C14
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 5818460
zbMATH Keywords: minimum drag work
zbMATH Keywords: ordinary differential equation
zbMATH Keywords: symmetry
zbMATH Keywords: classification
MaRDI profile type: Publication
full work available at URL: s10483-010-1325-x
OpenAlex ID: W2043363103
Wikidata QID: Q58206662
cites work: Symmetries and differential equations
cites work: Q4692893
cites work: CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
cites work: Symmetry group classification of ordinary differential equations: Survey of some results
DOI: 10.1007/S10483-010-1325-X
description: scientific article; zbMATH DE number 5818460