Journal of Nonlinear Mathematical Physics

Volume 17, Issue 2, June 2010, Pages 167 - 178

Lagrangians for Dissipative Nonlinear Oscillators: The Method of Jacobi Last Multiplier

Authors
M. C. Nucci
Dipartimento di Matematica e Informatica, Università di Perugia, 06123 Perugia, Italy,nucci@unipg.it
K. M. Tamizhmani
Department of Mathematics, Pondicherry University, Kalapet, Puducherry, 605 014, India,tamizh@yahoo.com
Received 22 June 2009, Accepted 29 September 2009, Available Online 7 January 2021.
DOI
10.1142/S1402925110000696How to use a DOI?
Keywords
Ordinary differential equations; Lie symmetry algebra; Lagrangian
Abstract

We present a method devised by Jacobi to derive Lagrangians of any second-order differential equation: it consists in finding a Jacobi Last Multiplier. We illustrate the easiness and the power of Jacobi's method by applying it to several equations, including a class of equations recently studied by Musielak with his own method [Z. E. Musielak, Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients J. Phys. A: Math. Theor. 41 (2008) 055205], and in particular a Liènard type nonlinear oscillator and a second-order Riccati equation. Also, we derive more than one Lagrangian for each equation.

Copyright
© 2010 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
17 - 2
Pages
167 - 178
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925110000696How to use a DOI?
Copyright
© 2010 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  - K. M. Tamizhmani
PY  - 2021
DA  - 2021/01/07
TI  - Lagrangians for Dissipative Nonlinear Oscillators: The Method of Jacobi Last Multiplier
JO  - Journal of Nonlinear Mathematical Physics
SP  - 167
EP  - 178
VL  - 17
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925110000696
DO  - 10.1142/S1402925110000696
ID  - Nucci2021
ER  -