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The integrability conditions in the inverse problem of the calculus of variations for second-order ordinary differential equations

Willy Sarlet UGent, Michael Crampin and E Martínez (1998) ACTA APPLICANDAE MATHEMATICAE. 54(3). p.233-273
abstract
A novel approach to a coordinate-free analysis of the multiplier question in the inverse problem of the calculus of variations, initiated in a previous publication, is completed in the following sense: under quite general circumstances, the complete set of passivity or integrability conditions is computed for systems with arbitrary dimension n. The results are applied to prove that the problem is always solvable in the case that the Jacobi endomorphism of the system is a multiple of the identity. This generalizes to arbitrary n a result derived by Douglas for n = 2.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
inverse problem, Lagrangian systems, integrability, TANGENT BUNDLE, DERIVATIONS, DYNAMICS, SYSTEMS, FORMS
journal title
ACTA APPLICANDAE MATHEMATICAE
Acta Appl. Math.
volume
54
issue
3
pages
233 - 273
Web of Science type
Article
Web of Science id
000078594700001
ISSN
0167-8019
DOI
10.1023/A:1006102121371
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
174088
handle
http://hdl.handle.net/1854/LU-174088
date created
2004-01-14 13:40:00
date last changed
2016-12-19 15:38:09
@article{174088,
  abstract     = {A novel approach to a coordinate-free analysis of the multiplier question in the inverse problem of the calculus of variations, initiated in a previous publication, is completed in the following sense: under quite general circumstances, the complete set of passivity or integrability conditions is computed for systems with arbitrary dimension n. The results are applied to prove that the problem is always solvable in the case that the Jacobi endomorphism of the system is a multiple of the identity. This generalizes to arbitrary n a result derived by Douglas for n = 2.},
  author       = {Sarlet, Willy and Crampin, Michael and Mart{\'i}nez, E},
  issn         = {0167-8019},
  journal      = {ACTA APPLICANDAE MATHEMATICAE},
  keyword      = {inverse problem,Lagrangian systems,integrability,TANGENT BUNDLE,DERIVATIONS,DYNAMICS,SYSTEMS,FORMS},
  language     = {eng},
  number       = {3},
  pages        = {233--273},
  title        = {The integrability conditions in the inverse problem of the calculus of variations for second-order ordinary differential equations},
  url          = {http://dx.doi.org/10.1023/A:1006102121371},
  volume       = {54},
  year         = {1998},
}

Chicago
Sarlet, Willy, Michael Crampin, and E Martínez. 1998. “The Integrability Conditions in the Inverse Problem of the Calculus of Variations for Second-order Ordinary Differential Equations.” Acta Applicandae Mathematicae 54 (3): 233–273.
APA
Sarlet, Willy, Crampin, M., & Martínez, E. (1998). The integrability conditions in the inverse problem of the calculus of variations for second-order ordinary differential equations. ACTA APPLICANDAE MATHEMATICAE, 54(3), 233–273.
Vancouver
1.
Sarlet W, Crampin M, Martínez E. The integrability conditions in the inverse problem of the calculus of variations for second-order ordinary differential equations. ACTA APPLICANDAE MATHEMATICAE. 1998;54(3):233–73.
MLA
Sarlet, Willy, Michael Crampin, and E Martínez. “The Integrability Conditions in the Inverse Problem of the Calculus of Variations for Second-order Ordinary Differential Equations.” ACTA APPLICANDAE MATHEMATICAE 54.3 (1998): 233–273. Print.