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/).
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 -