Journal of Nonlinear Mathematical Physics

Volume 16, Issue 4, March 2013, Pages 431 - 441

An Old Method of Jacobi to Find Lagrangians

Authors
M. C. Nucci
Dipartimento di Matematica e Informatica, Università di Perugia, 06123 Perugia, Italy, nucci@unipg.it
P. G. L. Leach
School of Mathematical Sciences, Westville Campus, University of KwaZulu-Natal, Durban 4000, Republic of South Africa, leachp@nu.ac.za, leachp@math.aegean.gr
Received 12 December 2008, Accepted 26 March 2009, Available Online 7 January 2021.
DOI
https://doi.org/10.1142/S1402925109000467How to use a DOI?
Keywords
Lagrangian, Jacobi last multiplier, Lie symmetry, Noether symmetry
Abstract

In a recent paper by Ibragimov a method was presented in order to find Lagrangians of certain second-order ordinary differential equations admitting a two-dimensional Lie symmetry algebra. We present a method devised by Jacobi which enables one to derive (many) Lagrangians of any second-order differential equation. The method is based on the search of the Jacobi Last Multipliers for the equations. We exemplify the simplicity and elegance of Jacobi's method by applying it to the same two equations as Ibragimov did. We show that the Lagrangians obtained by Ibragimov are particular cases of some of the many Lagrangians that can be obtained by Jacobi’s method.

Copyright
© 2009 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
16 - 4
Pages
431 - 441
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925109000467How to use a DOI?
Copyright
© 2009 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - M. C. Nucci
AU  - P. G. L. Leach
PY  - 2021
DA  - 2021/01
TI  - An Old Method of Jacobi to Find Lagrangians
JO  - Journal of Nonlinear Mathematical Physics
SP  - 431
EP  - 441
VL  - 16
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925109000467
DO  - https://doi.org/10.1142/S1402925109000467
ID  - Nucci2021
ER  -